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g(stabilit) n(y) g(of) h(exosolar) 486 3491 y(planetary) h(systems.) h(In) f(particular,) i(w) n(e) g(study) e (the) g(stabilit) n(y) i(of) f(Earth-lik) n(e) g(planets) h(in) e(the) 486 3582 y(planetary) g(systems) g(HD168746,) j(GI86,) e(47UMa,b) h (and) f(HD10697.) p Fs 486 3744 a(Keyw) n(ords:) p Fr 28 w(P) n(erio) r(dic) h(orbits,) f(linear) h(stabilit) n(y) -6 b(,) 26 b(three-b) r(o) r(dy) f(problem,) g(exosolar) i(systems) p Fo 1515 4106 a(1.) 73 b(In) m(tro) s(duction) p Fv 486 4309 a(The) 46 b(three-b) s(o) s(dy) g(problem) f(is) h(a) h(con) m (tin) m(uous) g(source) g(of) g(study) -8 b(,) 47 b(since) f(the) 486 4417 y(disco) m(v) m(ery) 39 b(of) g(its) g(non-in) m(tegrabilit) m(y) e (due) h(to) i(H.) f(P) m(oincar) m(\023) -43 b(e) 41 b(\(1892\).) g(Regular) 486 4525 y(and) d(c) m(haotic) j(motions) e(ha) m(v) m(e) h(b) s(een) f(widely) e(in) m(v) m(estigated) j(with) e(an) m (y) h(kind) f(of) 486 4633 y(to) s(ols,) 26 b(from) g(analytical) f (results) h(to) h(n) m(umerical) 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Ai"3B!'gY~> @endspecial Fr 706 5066 a(c) p Fp 685 5068 a(\015) p Fr 25 w(2001) p Ft 27 w(Kluwer) 28 b(A) l(c) l(ademic) g (Publishers.) 56 b(Printe) l(d) 28 b(in) f(the) i(Netherlands.) p Fn 1941 5847 a(cchv-r5.tex;) 42 b(27/09/2001;) g(9:54;) e(p.1) p 90 rotate dyy eop %%Page: 2 2 2 1 bop Fv 486 100 a(2) 486 291 y(system,) 29 b(puzzled) f(scien) m (tists) g(and) h(still) e(remains) h(one) h(of) g(the) g(most) h(in) m (teresting) 486 399 y(sub) 5 b(jects) 36 b(of) i(Celestial) e(Mec) m (hanics.) i(In) f(particular,) f(the) h(explanation) f(of) i(the) 486 506 y(fact) c(that) g(in) e(the) i(asteroid) f(b) s(elt) f(some) i (resonances) g(are) g(empt) m(y) f(while) f(others) 486 614 y(are) e(w) m(ell) g(p) s(opulated) e(has) j(b) s(een) e(un) m(til) g(recen) m(tly) i(an) f(op) s(en) f(problem.) 602 722 y(In) 22 b(this) g(pap) s(er,) g(w) m(e) h(consider) f(the) h(planar,) f (circular,) f(restricted,) i(three-b) s(o) s(dy) 486 830 y(problem,) g(where) i(w) m(e) g(assume) g(that) g(the) h(mass) e (of) i(one) f(b) s(o) s(dy) e(is) h(so) h(small) f(that) h(it) 486 938 y(do) s(es) g(not) h(in\015uence) e(the) i(motion) f(of) h(the) g (other) g(t) m(w) m(o) h(b) s(o) s(dies,) d(called) h(primaries.) 486 1046 y(Let) 40 b(the) h(three) f(b) s(o) s(dies) f(b) s(e) g(named) h (as) p Fm 41 w(S) p Fv 5 w(,) p Fm 40 w(J) p Fv 9 w(,) p Fm 41 w(A) p Fv(,) g(later) g(iden) m(ti\014ed) f(with) g(the) 486 1154 y(Sun,) 28 b(Jupiter) g(and) h(an) h(asteroid.) f(W) -8 b(e) 31 b(assume) f(that) g(the) g(motion) f(of) p Fm 30 w(J) p Fv 39 w(around) p Fm 486 1262 a(S) p Fv 31 w(is) c(circular) f(and) h(that) i(all) e(b) s(o) s(dies) f(mo) m(v) m (e) k(on) e(the) g(same) g(plane.) g(Let) g(us) f(denote) 486 1370 y(b) m(y) p Fm 29 w(n) p Fv(,) p Fm 30 w(n) p Fl 776 1337 a(0) p Fv 829 1370 a(the) 30 b(mean) g(motions) f(of) p Fm 30 w(A) p Fv 30 w(and) p Fm 30 w(J) p Fv 9 w(,) h(resp) s(ectiv) m (ely) -8 b(.) 30 b(W) -8 b(e) 31 b(will) c(w) m(ork) j(in) f(a) 486 1478 y(syno) s(dic) 23 b(frame,) i(rotating) g(with) f(the) h(same) h (angular) e(v) m(elo) s(cit) m(y) h(of) g(the) g(primaries) p Fm 486 1586 a(S) p Fv 35 w(and) p Fm 30 w(J) p Fv 9 w(,) 30 b(whic) m(h) f(are) i(assumed) f(to) h(b) s(e) f(at) h(rest) f(on) h (the) p Fm 30 w(x) p Fv(-axis.) 602 1694 y(A) p Fm 34 w(p=q) p Fv 38 w(resonance) k(is) f(a) h(p) s(erio) s(dic) c(orbit) j (suc) m(h) g(that) i(the) e(ratio) p Fm 35 w(n=n) p Fl 2996 1661 a(0) p Fv 3053 1694 a(is) g(ap-) 486 1802 y(pro) m(ximately) 25 b(equal) i(to) p Fm 27 w(p=q) p Fv 29 w(for) g(some) g(p) s(ositiv) m (e) e(in) m(tegers) p Fm 27 w(p) p Fv(,) p Fm 26 w(q) p Fv 3 w(.) i(W) -8 b(e) 28 b(ha) m(v) m(e) f(exact) 486 1910 y(equalit) m(y) -8 b(,) p Fm 28 w(n=n) p Fl 1002 1877 a(0) p Fv 1050 1910 a(=) p Fm 25 w(p=q) p Fv 3 w(,) 28 b(when) f(the) i(mass) f(of) g(the) g(small) f(primary) p Fm 26 w(J) p Fv 37 w(is) h(equal) f(to) 486 2017 y(zero.) j(Indeed,) e (for) h(an) m(y) p Fm 29 w(p) p Fv 29 w(and) p Fm 28 w(q) p Fv 32 w(there) g(exist) g(t) m(w) m(o) h(families) d(of) j(p) s (erio) s(dic) c(orbits) 486 2125 y(whic) m(h) 36 b(di\013er) g(in) g (phase) h(and) g(are) h(generated) h(b) m(y) e(a) h(v) -5 b(ariation) 37 b(of) g(the) h(orbital) 486 2233 y(eccen) m(tricit) m(y) 31 b(of) g(the) f(small) f(b) s(o) s(dy) p Fm 29 w(A) p Fv(.) 602 2341 y(Our) 34 b(aim) h(is) f(to) i(in) m(v) m(estigate) g (the) g(stabilit) m(y) e(of) h(these) h(families) d(of) j(p) s(erio) s (dic) 486 2449 y(orbits) 45 b(\(see) j(Hadjidemetriou) d(and) h(Ic) m (h) m(tiaroglou) h(\(1984\),) j(Hadjidemetriou) 486 2557 y(\(1988\),) 41 b(\(1992\),) h(\(1996\),) f(Win) m(ter) e(and) f(Murra) m(y) h(\(1997\),) i(\(1997\)) h(and) c(refer-) 486 2665 y(ences) 25 b(therein\).) f(The) h(linear) e(stabilit) m(y) g(of) i(a) h (p) s(erio) s(dic) c(orbit) i(can) h(b) s(e) f(studied) f(b) m(y) 486 2773 y(lo) s(oking) h(at) j(the) g(eigen) m(v) -5 b(alues) 26 b(of) g(the) g(mono) s(drom) m(y) g(matrix) f(along) h(the) h(p) s (erio) s(dic) 486 2881 y(orbit) 42 b(itself.) h(By) h(computing) f(the) g(trace) i(of) f(the) g(matrix) f(w) m(e) h(can) g(conclude) 486 2989 y(whether) 34 b(a) h(p) s(erio) s(dic) e(orbit) h(is) g(linearly) e (stable) j(or) g(not.) g(The) g(mo) s(del) e(and) i(the) 486 3097 y(metho) s(d) 29 b(to) i(study) f(linear) f(stabilit) m(y) g(are) i (presen) m(ted) f(in) p Fk 29 w(x) p Fv(2.) 602 3205 y(The) d(\014rst) h(part) f(of) i(this) e(w) m(ork) h(deals) f(with) g (the) h(analysis) f(of) h(the) g(stabilit) m(y) f(as) 486 3313 y(the) 32 b(mass) h(of) g(the) g(primaries) d(is) i(\014xed.) g (In) g(particular,) g(w) m(e) h(consider) e(the) i(Sun-) 486 3421 y(Jupiter) 21 b(system) i(and) g(w) m(e) h(in) m(v) m(estigate) g (the) f(stabilit) m(y) f(of) i(inner) d(and) i(outer) g(orbits) 486 3528 y(\(i.e.,) 37 b(in) m(terior) e(and) h(exterior) g(resonances\).) i (W) -8 b(e) 37 b(presen) m(t) g(results) e(for) h(v) -5 b(arious) 486 3636 y(v) g(alues) 32 b(of) p Fm 33 w(p=q) p Fv 36 w(with) f(2) p Fk 30 w(\024) p Fm 29 w(p) p Fk 29 w(\024) p Fv 29 w(9,) j(1) p Fk 30 w(\024) p Fm 29 w(q) p Fk 32 w(\024) p Fv 29 w(5) f(and) f(4) p Fm(=) p Fv(3) p Fk 31 w(\024) p Fm 29 w(p=q) p Fk 33 w(\024) p Fv 29 w(5.) h(F) -8 b(or) 34 b(eac) m(h) 486 3744 y(family) 42 b(of) i(p) s(erio) s(dic) d(orbits) i(with) g(frequency) p Fm 43 w(p=q) p Fv 47 w(w) m(e) h(compute) h(the) f(linear) 486 3852 y(stabilit) m(y) 39 b(as) i(a) h(function) d(of) j(the) f(a) m(v) m (erage) i(eccen) m(tricit) m(y) f(along) f(the) h(p) s(erio) s(dic) 486 3960 y(orbit.) 23 b(There) h(are) g(mark) m(ed) g(di\013erences) g(in) e (the) j(stabilit) m(y) d(b) s(eha) m(viour) h(according) 486 4068 y(to) 37 b(the) g(v) -5 b(alue) 36 b(of) p Fm 37 w(p=q) p Fv 3 w(;) h(in) f(particular,) f(w) m(e) i(noticed) g(that) g (switc) m(hing) e(b) s(et) m(w) m(een) 486 4176 y(stabilit) m(y) 29 b(and) h(instabilit) m(y) e(o) s(ccurs) i(more) g(frequen) m(tly) g(as) p Fm 31 w(q) p Fv 33 w(gets) i(larger.) e(These) 486 4284 y(results) f(are) h(describ) s(ed) f(in) p Fk 29 w(x) p Fv(3.) 602 4392 y(A) 43 b(study) f(of) i(the) f(stabilit) m(y) f (c) m(haracter) j(as) e(the) h(mass) f(of) g(the) h(primary) d(is) 486 4500 y(v) -5 b(aried,) 38 b(is) g(presen) m(ted) h(is) p Fk 38 w(x) p Fv(4.) h(This) d(analysis) h(is) g(particularly) e(suited) i(for) h(the) 486 4608 y(in) m(v) m(estigation) 48 b(of) g(exosolar) g (planetary) g(systems,) g(where) f(the) i(mass) f(of) g(the) 486 4716 y(primary) c(cannot) k(b) s(e) e(determined) f(with) h(accuracy) -8 b(,) 48 b(due) e(to) i(the) e(unkno) m(wn) 486 4824 y(inclination) 21 b(of) k(the) g(plane) f(of) g(motion.) h(Also) f(in) g(this) f(case) j (w) m(e) f(in) m(v) m(estigate) h(inner) p Fn 1941 5847 a(cchv-r5.tex;) 42 b(27/09/2001;) g(9:54;) e(p.2) p 90 rotate dyy eop %%Page: 3 3 3 2 bop Fv 3230 100 a(3) 486 291 y(and) 32 b(outer) h(orbits,) f(pro) m (viding) f(a) j(description) d(of) i(the) g(stabilit) m(y) f(c) m (haracter) i(for) 486 399 y(di\013eren) m(t) 29 b(v) -5 b(alues) 30 b(of) h(the) f(masses) h(and) e(eccen) m(tricities.) 602 506 y(As) 37 b(a) g(concluding) f(result,) g(w) m(e) h(apply) f(the) h (analysis) f(to) i(the) f(p) s(ossibilit) m(y) d(of) 486 614 y(existence) 23 b(of) g(stable) f(Earth-lik) m(e) g(planets) g(in) g (the) h(recen) m(tly) g(disco) m(v) m(ered) g(exosolar) 486 722 y(systems) 30 b(HD168746,) k(GI86,) d(47UMa,b) h(and) e(HD10697.) p Fo 1346 1043 a(2.) 73 b(Mo) s(del) 36 b(and) e(metho) s(ds) p Fv 486 1257 a(2.1.) p Fj 65 w(Equa) -6 b(tions) 33 b(of) h(motion) p Fv 486 1449 a(W) -8 b(e) 23 b(consider) e(three) i(b) s(o) s(dies) p Fm 20 w(S) p Fv 5 w(,) p Fm 23 w(J) p Fv 9 w(,) p Fm 22 w(A) p Fv(;) g(for) f(later) h(applications) d(w) m(e) j(shall) e (iden) m(tify) p Fm 486 1557 a(S) p Fv 36 w(with) 30 b(the) h(Sun,) p Fm 30 w(J) p Fv 41 w(with) f(Jupiter) f(and) p Fm 31 w(A) p Fv 32 w(with) h(a) h(small) f(b) s(o) s(dy) g(of) h (negligible) 486 1665 y(mass.) 44 b(Let) p Fm 44 w(m) p Fi 1004 1679 a(S) p Fv 1098 1665 a(and) p Fm 44 w(m) p Fi 1369 1679 a(J) p Fv 1461 1665 a(b) s(e) f(the) i(masses) f(of) p Fm 44 w(S) p Fv 48 w(and) p Fm 44 w(J) p Fv 9 w(,) g(resp) s(ectiv) m (ely) -8 b(.) 44 b(W) -8 b(e) 486 1773 y(assume) 40 b(that) g(the) h (three) f(b) s(o) s(dies) e(mo) m(v) m(e) k(on) e(the) h(same) f(plane) f(and) h(that) h(the) 486 1881 y(orbit) c(of) p Fm 38 w(J) p Fv 48 w(is) g(circular.) g(W) -8 b(e) 40 b(refer) e(to) h(this) e (mo) s(del) g(as) i(the) f(planar,) f(circular,) 486 1989 y(restricted) h(three-b) s(o) s(dy) g(problem,) f(hereafter,) i (PCR3BP) -8 b(.) 40 b(Let) f(us) f(normalize) 486 2097 y(the) 31 b(units) f(so) i(that) g(the) g(distance) f(b) s(et) m(w) m (een) h(the) g(primaries,) d(the) j(sum) e(of) i(their) 486 2205 y(masses) e(and) g(the) g(gra) m(vitational) h(constan) m(t) h (are) e(equal) g(to) h(1.) 602 2313 y(W) -8 b(e) 23 b(consider) d(a) i (syno) s(dic) e(reference) j(frame) e(\() p Fm(O) s(xy) p Fv 3 w(\),) h(rotating) g(with) f(the) h(same) 486 2421 y(frequency) 35 b(of) h(the) g(primaries.) d(Let) k(the) f(origin) e (coincide) h(with) f(the) i(cen) m(ter) h(of) 486 2529 y(mass) 23 b(of) h(the) g(primaries) d(and) i(let) h(the) p Fm 23 w(x) p Fv(-axis) g(corresp) s(ond) e(to) j(the) p Fm 23 w(S) 5 b(J) p Fv 33 w(direction.) 486 2637 y(Denote) 32 b(b) m(y) f(\() p Fm(x;) 15 b(y) p Fv 3 w(\)) 32 b(the) g(co) s (ordinates) e(of) p Fm 32 w(A) p Fv 31 w(and) g(b) m(y) p Fm 31 w(\026) p Fv 31 w(the) i(reduced) e(mass) p Fm 31 w(\026) p Fk 26 w(\021) p Fm 486 2745 a(m) p Fi 566 2759 a(J) p Fm 614 2745 a(=) p Fv(\() p Fm(m) p Fi 774 2759 a(s) p Fv 829 2745 a(+) p Fm 18 w(m) p Fi 998 2759 a(J) p Fv 1046 2745 a(\).) g(The) f(equations) f(of) i(motion) f(of) p Fm 29 w(A) p Fv 29 w(in) f(the) h(syno) s(dic) f(reference) 486 2853 y(frame) i(are) h(giv) m(en) f(b) m(y) g(Szeb) s(ehely) f (\(1967\)) 1016 3082 y(\177) p Fm -51 w(x) p Fk 20 w(\000) p Fv 20 w(2) 17 b(_) p Fm -42 w(y) p Fk 24 w(\000) p Fm 20 w(x) p Fv 49 w(=) p Fk 50 w(\000) p Fm(\026) 1736 3021 y(x) p Fv 19 w(+) p Fm 20 w(\026) p Fk 20 w(\000) p Fv 20 w(1) p 1736 3061 375 4 v Fm 1881 3146 a(r) p Fh 1925 3114 a(3) 1922 3170 y(1) p Fk 2140 3082 a(\000) p Fv 20 w(\(1) p Fk 21 w(\000) p Fm 20 w(\026) p Fv(\)) p Fm 2523 3021 a(x) p Fv 20 w(+) p Fm 20 w(\026) p 2523 3061 218 4 v 2590 3146 a(r) p Fh 2634 3114 a(3) 2631 3170 y(2) p Fv 1020 3304 a(\177) p Fm -51 w(y) p Fv 23 w(+) j(2) c(_) p Fm -41 w(x) p Fk 21 w(\000) p Fm 20 w(y) p Fv 52 w(=) p Fk 50 w(\000) p Fm(\026) 1753 3243 y(y) p 1736 3283 83 4 v 1736 3367 a(r) p Fh 1780 3336 a(3) 1777 3392 y(1) p Fk 1848 3304 a(\000) p Fv 20 w(\(1) p Fk 21 w(\000) p Fm 20 w(\026) p Fv(\)) p Fm 2249 3243 a(y) p 2231 3283 V 2231 3367 a(r) p Fh 2275 3336 a(3) 2272 3392 y(2) p Fm 2324 3304 a(;) p Fv 486 3555 a(where) p Fm 35 w(r) p Fh 798 3522 a(2) 795 3578 y(1) p Fv 871 3555 a(=) 34 b(\() p Fm(x) p Fv 24 w(+) p Fm 24 w(\026) p Fk 23 w(\000) p Fv 24 w(1\)) p Fh 1435 3522 a(2) p Fv 1499 3555 a(+) p Fm 24 w(y) p Fh 1642 3522 a(2) p Fv 1681 3555 a(,) p Fm 36 w(r) p Fh 1786 3522 a(2) 1783 3578 y(2) p Fv 1859 3555 a(=) g(\() p Fm(x) p Fv 24 w(+) p Fm 24 w(\026) p Fv(\)) p Fh 2260 3522 a(2) p Fv 2323 3555 a(+) p Fm 24 w(y) p Fh 2466 3522 a(2) p Fv 2505 3555 a(.) i(As) g(is) e(w) m(ell) h(kno) m(wn,) 486 3663 y(these) 30 b(equations) g(admit) g(the) h(\014rst) e(in) m(tegral) h (\(Jacobian) h(energy\)) p Fm 818 3893 a(C) p Fk 31 w(\021) p Fv 1020 3831 a(1) p 1020 3872 46 4 v 1020 3955 a(2) p Fg 1091 3799 a(\020) p Fv 1156 3893 a(_) p Fm -40 w(x) p Fh 1193 3855 a(2) p Fv 1252 3893 a(+) 36 b(_) p Fm -41 w(y) p Fh 1391 3855 a(2) p Fg 1430 3799 a(\021) p Fk 1500 3893 a(\000) p Fv 1601 3831 a(1) p 1601 3872 V 1601 3955 a(2) p Fg 1672 3799 a(h) p Fm 1711 3893 a(\026r) p Fh 1810 3855 a(2) 1807 3915 y(1) p Fv 1869 3893 a(+) 20 b(\(1) p Fk 21 w(\000) p Fm 19 w(\026) p Fv(\)) p Fm(r) p Fh 2285 3855 a(2) 2282 3915 y(2) p Fg 2325 3799 a(i) p Fk 2384 3893 a(\000) p Fm 2498 3831 a(\026) p 2485 3872 81 4 v 2485 3955 a(r) p Fh 2526 3969 a(1) p Fk 2595 3893 a(\000) p Fv 2696 3831 a(1) p Fk 21 w(\000) p Fm 20 w(\026) p 2696 3872 212 4 v 2762 3955 a(r) p Fh 2803 3969 a(2) p Fm 2918 3893 a(:) p Fv 486 4224 a(2.2.) p Fj 65 w(Mirr) n(or) 33 b(configura) -6 b(tions) p Fv 486 4417 a(In) 32 b(the) i(syno) s(dic) e (frame,) i(there) g(exist) f(families) f(of) i(p) s(erio) s(dic) d (orbits) h(inside) g(the) 486 4525 y(orbit) i(of) p Fm 36 w(J) p Fv 44 w(that) i(are) g(symmetric) e(with) g(resp) s(ect) i (to) g(the) p Fm 35 w(x) p Fv(-axis) f(\(notice) h(that) 486 4633 y(in) 30 b(general) h(these) h(orbits) f(are) h(not) f(symmetric) g (in) f(the) i(inertial) e(frame\).) i(If) f(the) 486 4741 y(initial) 39 b(conditions) h(are) j(suc) m(h) e(that) i(the) f(p) s(erio) s(dic) d(orbit) i(in) m(tersects) i(p) s(erp) s(en-) 486 4848 y(dicularly) 35 b(the) p Fm 39 w(x) p Fv(-axis) j(at) p Fm 39 w(t) p Fv 39 w(=) h(0) f(\(i.e.,) p Fm 40 w(y) p Fv 3 w(\(0\)) h(=) g(0,) 55 b(_) p Fm -41 w(x) p Fv(\(0\)) 40 b(=) e(0\),) i(the) f(p) s(erio) s(dic) p Fn 1941 5847 a(cchv-r5.tex;) j(27/09/2001;) g(9:54;) e(p.3) p 90 rotate dyy eop %%Page: 4 4 4 3 bop Fv 486 100 a(4) p Fr 1290 259 a(T) -6 b(able) 19 b(I.) 39 b(Numeric) 18 b(co) r(ding) h(of) h(MCs) g(for) 1290 350 y(in) n(terior) h(p) r(erio) r(dic) h(orbits) g(\(see) f(the) f (text) 1290 441 y(for) 26 b(an) g(explanation) g(of) g(sym) n(b) r (ols\)) p 1290 519 1182 4 v 1340 617 a(Con\014guration) 114 b(MC) p Fq 125 w(l) p Fr 125 w(\001) p Fq(\025) p 1290 682 V Fr 1340 779 a(PC-SAJ) 325 b(00) 143 b(0) 152 b(0) 1340 888 y(PC-ASJ) 325 b(02) 143 b(0) p Fq 148 w(\031) p Fr 1340 997 a(A) n(C-SAJ) 321 b(20) p Fq 139 w(\031) p Fr 150 w(0) 1340 1106 y(A) n(C-ASJ) g(22) p Fq 139 w(\031) 146 b(\031) p 1290 1171 V Fv 486 1561 a(orbit) 37 b(in) m(tersects) i(p) s (erp) s(endicularly) 34 b(the) p Fm 39 w(x) p Fv(-axis) k(also) h(at) g (a) g(half) f(p) s(erio) s(d) e(\(i.e.,) p Fm 486 1669 a(y) p Fv 3 w(\() p Fm(T) 10 b(=) p Fv(2\)) 36 b(=) f(0,) 52 b(_) p Fm -41 w(x) p Fv(\() p Fm(T) 10 b(=) p Fv(2\)) 37 b(=) d(0,) j(where) p Fm 36 w(T) p Fv 48 w(denotes) g(the) f(p) s(erio) s(d) e(of) i(the) h(p) s(erio) s(dic) 486 1777 y(orbit\).) 602 1885 y(These) 25 b(in) m(tersections) h(represen) m(t) g(particular) e (cases) i(of) g(the) g(so-called) p Ff 26 w(mirror) 486 1993 y(con\014guration) p Fv 37 w(\(MC\),) 40 b(whic) m(h) d(o) s (ccurs) h(whenev) m(er) g(the) h(v) m(elo) s(cit) m(y) g(v) m(ectors) h (of) f(a) 486 2101 y(n) m(um) m(b) s(er) 26 b(of) i(gra) m (vitationally) f(in) m(teracting) h(b) s(o) s(dies) e(are) i(p) s(erp) s (endicular) 23 b(to) 29 b(their) 486 2209 y(p) s(osition) g(v) m (ectors) k(in) e(a) h(barycen) m(tric) g(sidereal) e(frame.) i(It) g(w) m(as) g(pro) m(v) m(en) g(b) m(y) f(Ro) m(y) 486 2317 y(and) 36 b(Ov) m(enden) h(\(1955\)) j(that) f(an) e(orbit) g(is) f(p) s (erio) s(dic) f(if) i(a) h(MC) f(o) s(ccurs) g(at) i(t) m(w) m(o) 486 2425 y(di\013eren) m(t) 29 b(ep) s(o) s(c) m(hs.) 602 2533 y(Mirror) 35 b(con\014gurations) h(can) h(b) s(e) f(classi\014ed) f (according) i(to) g(the) g(initial) d(p) s(o-) 486 2640 y(sitions) j(of) i(the) g(three) g(b) s(o) s(dies;) f(in) f (particular,) p Fm 38 w(A) p Fv 39 w(could) h(b) s(e) g(at) p Fm 40 w(t) p Fv 39 w(=) i(0) f(at) h(its) 486 2748 y(p) s(ericen) m (ter) j(\() p Fm(P) 13 b(C) p Fv 7 w(\)) 45 b(or) f(at) h(ap) s(o) s (cen) m(ter) g(\() p Fm(AC) p Fv 7 w(\)) f(and) g(the) g(initial) e (con\014guration) 486 2856 y(migh) m(t) 32 b(b) s(e) p Fm 32 w(S) p Fk 27 w(\000) p Fm 21 w(A) p Fk 22 w(\000) p Fm 21 w(J) p Fv 42 w(or) p Fm 33 w(A) p Fk 22 w(\000) p Fm 21 w(S) p Fk 27 w(\000) p Fm 21 w(J) p Fv 9 w(.) h(According) g(to) g (a) g(sc) m(heme) h(in) m(tro) s(duced) 486 2964 y(b) m(y) 27 b(V) -8 b(alsecc) m(hi) 29 b(et) g(al.) f(\(1993\),) j(it) c(is) g(p) s (ossible) f(to) j(co) s(de) f(all) f(p) s(ossible) e(MC's) k(using) 486 3072 y(a) h(pair) f(of) h(in) m(tegers,) h(indicating) d(the) i(v) -5 b(alue,) 30 b(in) f(m) m(ultiples) f(of) p Fm 30 w(\031) s(=) p Fv(2,) k(of) e(suitably) 486 3180 y(c) m(hosen) 22 b(angles;) f(this) f (is) h(done) g(in) f(T) -8 b(able) 21 b(I,) h(where) p Fm 21 w(l) p Fv 23 w(denotes) g(the) g(mean) f(anomaly) 486 3288 y(of) p Fm 34 w(A) p Fv 35 w(and) 34 b(\001) p Fm(\025) p Fv 34 w(is) f(the) i(di\013erence) f(of) h(the) f(mean) h(longitudes) e (of) p Fm 35 w(A) p Fv 34 w(and) p Fm 34 w(J) p Fv 9 w(.) i(As) 486 3396 y(an) d(example,) g(consider) f(the) i(MC) f (denoted) h(b) m(y) f(02;) i(then) p Fm 32 w(l) p Fv 30 w(=) 28 b(0) 33 b(and) f(\001) p Fm(\025) p Fv 28 w(=) p Fm 29 w(\031) p Fv 3 w(,) 486 3504 y(whic) m(h) 26 b(means) i(that) p Fm 28 w(A) p Fv 28 w(is) f(at) i(its) e(p) s(ericen) m(ter) g(in) g(the) h(con\014guration) p Fm 27 w(A) p Fk 16 w(\000) p Fm 15 w(S) p Fk 20 w(\000) p Fm 15 w(J) p Fv 9 w(.) 602 3612 y(Let) p Fm 33 w(n=n) p Fl 922 3579 a(0) p Fv 975 3612 a(=) p Fm 29 w(p=q) p Fv 3 w(,) 33 b(where) p Fm 33 w(n) p Fv(,) p Fm 33 w(n) p Fl 1702 3579 a(0) p Fv 1758 3612 a(denote) g(the) g(mean) g(motions) g(of) p Fm 33 w(A) p Fv 33 w(and) p Fm 33 w(J) p Fv 9 w(,) 486 3720 y(resp) s(ectiv) m(ely) -8 b(.) 23 b(In) h(a) g(symmetric) f(p) s (erio) s(dic) e(orbit) i(asso) s(ciated) i(to) f(this) f(resonance,) 486 3828 y(t) m(w) m(o) 31 b(features) g(are) g(notew) m(orth) m(y:) p Fk 523 4023 a(\000) p Fm 73 w(l) p Fv 33 w(mak) m(es) p Fm 31 w(p) p Fv 30 w(complete) g(rev) m(olutions,) e(while) g(\001) p Fm(\025) p Fv 30 w(mak) m(es) p Fm 31 w(p) p Fk 20 w(\000) p Fm 20 w(q) p Fv 3 w(;) p Fk 523 4222 a(\000) p Fv 73 w(t) m(w) m(o) j(MCs) e(m) m(ust) g(o) s(ccur,) h(c) m(haracterized) g (b) m(y) g(di\013eren) m(t) f(co) s(des.) 486 4417 y(F) -8 b(ollo) m(wing) 26 b(V) -8 b(alsecc) m(hi) 27 b(et) g(al.) f(\(1993\),) k(w) m(e) d(note) g(that) g(the) g(parit) m(y) f(of) p Fm 27 w(p) p Fv 26 w(and) p Fm 26 w(p) p Fk 13 w(\000) p Fm 13 w(q) p Fv 486 4525 a(uniquely) e(determines) h(the) i(co) s(des) g (of) f(the) h(MC's) g(that) g(can) g(app) s(ear) f(together) i(in) 486 4633 y(a) i(giv) m(en) h(symmetric) e(p) s(erio) s(dic) f(orbit) i(\(I) g(and) g(I) s(I) f(p.o.) i(in) e(T) -8 b(able) 30 b(I) s(I\).) 602 4741 y(W) -8 b(e) 27 b(remark) f(that) g(in) f(the) h(follo) m(wing) e (w) m(e) i(shall) f(consider) f(only) p Ff 25 w(direct) p Fv 26 w(orbits,) 486 4848 y(whic) m(h) 29 b(mo) m(v) m(e) i(around) p Fm 30 w(S) p Fv 35 w(in) e(the) i(same) g(direction) e(of) p Fm 30 w(J) p Fv 9 w(.) p Fn 1941 5847 a(cchv-r5.tex;) 42 b(27/09/2001;) g(9:54;) e(p.4) p 90 rotate dyy eop %%Page: 5 5 5 4 bop Fv 3230 100 a(5) p Fr 1054 259 a(T) -6 b(able) 47 b(I) r(I.) 39 b(The) 47 b(pairing) h(of) g(MCs) h(within) e(p) r(erio) r (dic) 1054 350 y(orbits) p 1054 428 1654 4 v Fq 1103 526 a(p) p Fr(,) p Fq 26 w(p) p Fp 16 w(\000) p Fq 17 w(q) p Fr 148 w(o) r(dd,ev) n(en) 143 b(ev) n(en,o) r(dd) h(o) r(dd,o) r (dd) p 1054 591 V 1103 688 a(I) 26 b(p.o.) 283 b(00,20) 268 b(00,02) 256 b(00,22) 1103 797 y(I) r(I) 26 b(p.o.) 253 b(22,02) 268 b(22,20) 256 b(02,20) p 1054 862 V Fv 602 1220 a(It) 37 b(will) d(b) s(e) j(useful) e(in) g(our) i(analysis) e (to) j(compute) g(an) e(appro) m(ximate) i(v) -5 b(alue) 486 1328 y(of) 27 b(the) g(eccen) m(tricit) m(y) h(whic) m(h) d(causes) j (collisions) c(or) j(v) m(ery) g(close) g(encoun) m(ters) g(with) p Fm 486 1436 a(J) p Fv 9 w(.) 36 b(An) g(appro) m(ximate) h(v) -5 b(alue) 36 b(can) h(b) s(e) e(obtained) h(b) m(y) h(equating) f(the) g (ap) s(o) s(cen) m(ter) 486 1544 y(distance) 30 b(of) p Fm 30 w(A) p Fv 31 w(to) h(the) p Fm 30 w(S) 5 b(J) p Fv 40 w(distance,) 30 b(whic) m(h) f(in) g(our) h(units) f(is) g(1:) p Fm 1626 1706 a(a) p Fv(\(1) 21 b(+) p Fm 20 w(e) p Fv(\)) k(=) g(1) p Fm(:) p Fv 486 1867 a(By) 30 b(Kepler's) g(third) e(la) m(w,) i(w) m(e) h(de\014ne) f(a) h(collision) d(v) -5 b(alue) p Fm 29 w(e) p Fi 2497 1881 a(c) p Fv 2563 1867 a(as) p Fm 1569 2102 a(e) p Fi 1611 2116 a(c) p Fk 1671 2102 a(\021) p Fg 1767 1983 a(\022) p Fm 1838 2041 a(p) p 1838 2081 46 4 v 1839 2165 a(q) p Fg 1894 1983 a(\023) p Fe 1965 1979 a(2) p 1965 1991 31 4 v 1965 2032 a(3) p Fk 2030 2102 a(\000) p Fv 20 w(1) p Fm(:) p Fv 968 w(\(1\)) 486 2403 y(2.3.) p Fj 65 w(Numerical) 33 b(determina) -6 b(tion) 32 b(of) i(periodic) g(orbits) p Fv 486 2585 a(Let) 26 b(us) f(brie\015y) f(describ) s(e) g(the) i(metho) s(d) f (adopted) h(to) g(\014nd) e(a) i(p) s(erio) s(dic) d(orbit.) j(Let) 486 2693 y(us) i(\014x) h(the) h(v) -5 b(alues) 29 b(of) p Fm 29 w(\026) p Fv(,) p Fm 30 w(n=n) p Fl 1522 2660 a(0) p Fv 1570 2693 a(=) p Fm 25 w(p=q) p Fv 32 w(and) g(the) h(unp) s(erturb) s(ed) 25 b(eccen) m(tricit) m(y) p Fm 31 w(e) p Fh 3210 2707 a(0) p Fv 3250 2693 a(.) 602 2801 y(The) 49 b(initial) d (conditions) p Fm 48 w(x) p Fv(\(0\),) 67 b(_) p Fm -42 w(y) p Fv 3 w(\(0\)) 51 b(\(recall) e(that) p Fm 49 w(y) p Fv 3 w(\(0\)) 58 b(=) f(0,) 65 b(_) p Fm -40 w(x) p Fv -1 w(\(0\)) 58 b(=) 486 2909 y(0\)) 44 b(are) h(found) d(b) m(y) i(the) h(t) m(w) m(o-b) s(o) s(dy) f(appro) m(ximation.) f(The) g(p) s(erio) s (dic) f(orbit) h(is) 486 3017 y(computed) f(within) d(a) k(preassigned) e(accuracy) -8 b(,) 44 b(t) m(ypically) d(10) p Fl 2676 2984 a(\000) p Fh(12) p Fv 2807 3017 a(,) h(through) g(a) 486 3125 y(Newton-Raphson) i(metho) s(d,) g(whic) m(h) f(pro) m(vides) g (successiv) m(e) i(appro) m(ximations) 486 3233 y(of) 36 b(the) g(initial) d(conditions.) h(Care) i(m) m(ust) g(b) s(e) f(tak) m (en) i(at) g(whic) m(h) d(in) m(tersection) i(of) 486 3341 y(the) 26 b(orbit) g(with) f(the) p Fm 26 w(x) p Fv(-axis) h(one) h(c) m(hec) m(ks) h(for) e(the) h(p) s(erp) s (endicularit) m(y) 22 b(condition.) 486 3449 y(As) j(long) f(as) i(the) f(eccen) m(tricit) m(y) h(is) e(small,) g(the) i(n) m(um) m(b) s(er) d (of) j(in) m(tersections) e(is) g(equal) 486 3557 y(to) p Fm 28 w(p) p Fk 14 w(\000) p Fm 14 w(q) p Fv 3 w(;) i(ho) m(w) m(ev) m (er,) j(as) e(the) h(eccen) m(tricit) m(y) g(increases,) f(a) h(lo) s (op) e(migh) m(t) h(dev) m(elop) g(in) 486 3665 y(the) j(rotating) h (frame) f(and) g(the) g(n) m(um) m(b) s(er) g(of) g(in) m(tersections) g (increases.) 602 3773 y(As) 20 b(output,) h(the) g(program) f(pro) m (vides) g(the) h(initial) d(conditions) h(of) i(the) g(p) s(erio) s (dic) 486 3880 y(orbit,) 43 b(partial) f(deriv) -5 b(ativ) m(es) 43 b(whic) m(h) f(are) j(needed) e(for) g(the) h(stabilit) m(y) e (analysis) 486 3988 y(and) 30 b(the) h(a) m(v) m(erage) i(v) -5 b(alues) 30 b(of) h(the) g(semima) 5 b(jor) 30 b(axis,) h(the) g(eccen) m(tricit) m(y) h(and) e(the) 486 4096 y(ratio) p Fm 31 w(n=n) p Fl 859 4063 a(0) p Fv 914 4096 a(o) m(v) m(er) j(half) e(p) s (erio) s(d) e(of) j(the) g(p) s(erio) s(dic) d(orbit,) i(due) g(to) h (the) g(symmetry) 486 4204 y(assumption.) d(In) g(particular,) g(let) i (us) e(de\014ne) h(the) g(a) m(v) m(erage) j(eccen) m(tricit) m(y) f (as) p Fm 1452 4422 a(e) p Fk 26 w(\021) p Fv 1710 4361 a(1) p 1656 4401 155 4 v Fm 1656 4485 a(T) 10 b(=) p Fv(2) p Fg 1835 4307 a(Z) p Fi 1918 4334 a(T) e(=) p Fh(2) 1881 4496 y(0) p Fm 2057 4422 a(e) p Fv(\() p Fm(t) p Fv(\)) p Fm(dt;) p Fv 852 w(\(2\)) 486 4633 y(where) p Fm 35 w(T) p Fk 47 w(\031) p Fv 34 w(2) p Fm(\031) s(q) p Fv 39 w(is) 35 b(the) h(p) s(erio) s(d) d(of) j(motion.) g(The) f (exact) j(equalit) m(y) d(holds) f(for) p Fm 486 4741 a(\026) p Fv 25 w(=) 25 b(0,) j(and) g(the) h(deviation) e(from) h(the) g(equalit) m(y) g(is) f(larger) h(for) g(larger) g(v) -5 b(alues) 28 b(of) p Fm 486 4848 a(\026) p Fv 30 w(as) i(w) m(ell) g(as) g(when) g(w) m(e) g(are) h(close) g(to) g(a) g(collision.) p Fn 1941 5847 a(cchv-r5.tex;) 42 b(27/09/2001;) g(9:54;) e(p.5) p 90 rotate dyy eop %%Page: 6 6 6 5 bop Fv 486 100 a(6) 602 291 y(The) 47 b(n) m(umerical) g(program) h (to) g(compute) h(the) f(p) s(erio) s(dic) d(orbits) i(and) h(the) 486 399 y(ab) s(o) m(v) m(e) 42 b(quan) m(tities) f(w) m(as) h(kindly) d (made) i(a) m(v) -5 b(ailable) 41 b(to) h(all) f(the) h(authors) f(b) m (y) g(J.) 486 506 y(Hadjidemetriou.) 486 750 y(2.4.) p Fj 65 w(Linear) 34 b(st) -6 b(ability) p Fv 486 963 a(W) e(e) 33 b(in) m(v) m(estigate) g(the) f(linear) f(stabilit) m(y) g(of) h(the) g (families) e(of) j(p) s(erio) s(dic) c(orbits) i(b) m(y) 486 1071 y(lo) s(oking) 22 b(at) i(the) f(trace) i(of) e(the) h(4) p Fk 6 w(\002) p Fv 6 w(4) g(mono) s(drom) m(y) f(matrix.) g(In) f(the) i (unp) s(erturb) s(ed) 486 1179 y(case) 33 b(\() p Fm(\026) p Fv 30 w(=) c(0\)) k(of) g(a) p Fd 33 w(r) -5 b(esonant) 37 b(p) -5 b(erio) g(dic) 37 b(orbit) p Fv(,) c(there) g(exist) g(t) m(w) m (o) h(pairs) e(of) g(unit) 486 1287 y(eigen) m(v) -5 b(alues.) 602 1395 y(When) 37 b(the) g(p) s(erturbation) e(is) i(switc) m(hed) f(on) h(\() p Fm(\026) p Fk 37 w(6) p Fv(=) g(0\),) h(one) f (pair) f(of) i(eigen-) 486 1503 y(v) -5 b(alues) 36 b(surviv) m(es,) f (due) h(to) i(the) f(existence) g(of) g(the) g(Jacobian) f(energy) h (in) m(tegral.) 486 1611 y(Ho) m(w) m(ev) m(er,) k(the) e(other) g (unit) f(pair) g(has) g(t) m(w) m(o) j(p) s(ossibilities) 34 b(to) 40 b(ev) m(olv) m(e:) g(the) g(t) m(w) m(o) 486 1719 y(eigen) m(v) -5 b(alues) 27 b(can) i(mo) m(v) m(e) p Fd 29 w(on) i(the) g(unit) g(cir) -5 b(cle) p Fv(,) 28 b(and) g(form) f(a) i(complex) f(conjugate) 486 1826 y(pair) j(of) i(the) g(form) p Fm 32 w(e) p Fl 1199 1793 a(\006) p Fi(i\036) p Fv 1324 1826 a(,) g(or) f(mo) m(v) m(e) p Fd 35 w(on) j(the) g(r) -5 b(e) g(al) 36 b(axis) p Fv 33 w(and) c(form) g(a) h(real) g(pair) p Fm 31 w(\025) p Fv 486 1934 a(and) p Fm 29 w(\025) p Fl 715 1901 a(\000) p Fh(1) p Fv 810 1934 a(.) 602 2042 y(In) g(the) i(case) g(of) g(a) f (complex) g(conjugate) i(pair) d(on) h(the) h(unit) d(circle) i(w) m(e) h(ha) m(v) m(e) 486 2150 y(stabilit) m(y) -8 b(,) 28 b(while) f(in) g(the) i(case) h(of) g(a) f(pair) f(of) h(recipro) s (cal) e(real) i(n) m(um) m(b) s(ers) e(w) m(e) j(ha) m(v) m(e) 486 2258 y(instabilit) m(y) -8 b(.) 28 b(In) i(some) h(particular) e (cases,) j(the) f(second) g(unp) s(erturb) s(ed) c(unit) i(pair) 486 2366 y(also) 42 b(surviv) m(es) g(as) h(a) g(second) f(unit) g(pair.) f (This) g(is) h(a) h(critical) f(case) h(as) g(far) g(as) 486 2474 y(stabilit) m(y) i(is) h(concerned) h(and) g(it) f(is) g(a) i (transition) d(p) s(oin) m(t) h(from) h(stabilit) m(y) e(to) 486 2582 y(instabilit) m(y) 27 b(or) k(vicev) m(ersa.) 602 2690 y(The) 38 b(t) m(yp) s(e) h(of) f(stabilit) m(y) g(can) h(b) s(e) f (obtained) g(from) g(the) h(trace) g(of) g(the) g(mon-) 486 2798 y(o) s(drom) m(y) 27 b(matrix.) h(As) g(is) f(w) m(ell) g(kno) m (wn,) g(as) i(far) e(as) i(the) f(trace) h(is) e(in) f(mo) s(dulus) g (less) 486 2906 y(than) k(4) h(one) g(has) f(stabilit) m(y) -8 b(,) 30 b(while) f(if) h(it) g(is) g(greater) i(than) e(4) h(the) g(p) s (erio) s(dic) d(orbit) 486 3014 y(is) 36 b(unstable.) g(W) -8 b(e) 39 b(refer) e(to) p Ff 38 w(indi\013eren) m(t) e(equilibrium) p Fv 33 w(whenev) m(er) i(the) h(trace) g(is) 486 3122 y(exactly) 31 b(equal) f(to) h(4.) 602 3230 y(Instead) 41 b(of) h(computing) f(the) h(4) p Fk 28 w(\002) p Fv 28 w(4) g(mono) s(drom) m(y) f(matrix,) g(the) h(stabilit) m(y) 486 3337 y(can) 27 b(b) s(e) g(obtained) g(b) m(y) g(in) m(v) m(estigating) h(the) g(P) m(oincar) m(\023) -43 b(e) 29 b(map,) e(where) g(the) h(p) s (erio) s(dic) 486 3445 y(orbit) g(is) h(a) i(\014xed) e(p) s(oin) m(t.) g(More) h(precisely) -8 b(,) 29 b(\014x) h(the) g(Jacobian) f(energy) h (and) f(tak) m(e) 486 3553 y(the) d(surface) g(of) g(section) g (corresp) s(onding) e(to) p Fm 27 w(y) p Fv 28 w(=) h(0.) i(Then) e (the) h(map) f(is) h(in) e(a) j(t) m(w) m(o) 486 3661 y(dimensional) 33 b(space) j(\() p Fm(x) p Fv(,) 52 b(_) p Fm -41 w(x) p Fv(\).) 37 b(The) e(linear) f(stabilit) m(y) h(c) m (haracter) i(can) f(b) s(e) f(found) 486 3769 y(b) m(y) i(a) h(2) p Fk 25 w(\002) p Fv 25 w(2) f(matrix) g(and) g(it) g(can) g(b) s(e) g (pro) m(v) m(en) h(that) g(its) f(eigen) m(v) -5 b(alues) 37 b(coincide) 486 3877 y(with) 29 b(the) h(t) m(w) m(o) i(non) e(unit) f (eigen) m(v) -5 b(alues) 30 b(of) g(the) h(mono) s(drom) m(y) f (matrix.) 602 3985 y(Finally) -8 b(,) 37 b(let) i(us) e(remark) i(that) g(nonlinear) d(stabilit) m(y) i(can) g(b) s(e) g(in) m(v) m(estigated) 486 4093 y(b) m(y) 31 b(means) g(of) h(KAM) f(theory) h(\(Kolmogoro) m (v) h(\(1954\),) h(Arnol'd) c(\(1963\),) k(Moser) 486 4201 y(\(1962\)\),) 49 b(but) c(suc) m(h) h(an) h(analysis) d(go) s(es) j(b) s(ey) m(ond) f(the) g(aims) g(of) g(the) h(presen) m(t) 486 4309 y(w) m(ork.) e(Ho) m(w) m(ev) m(er,) i(the) e(nonlinear) e (stabilit) m(y) g(can) j(b) s(e) e(obtained) g(n) m(umerically) 486 4417 y(b) m(y) f(computing) f(the) i(P) m(oincar) m(\023) -43 b(e) 45 b(map) e(on) g(the) g(ab) s(o) m(v) m(e) i(surface) e(of) h (section.) f(If) 486 4525 y(around) 35 b(the) h(\014xed) f(p) s(oin) m (t) g(of) i(the) f(map,) g(i.e.) g(around) f(the) i(p) s(erio) s(dic) c (orbit,) j(w) m(e) 486 4633 y(ha) m(v) m(e) 31 b(islands,) e(then) h (the) h(motion) g(is) e(stable,) i(trapp) s(ed) f(inside) e(the) j (island.) e(The) 486 4741 y(size) h(of) g(the) h(largest) g(island) d (giv) m(es) j(the) g(nonlinear) d(stabilit) m(y) h(region.) h(If,) g (on) h(the) 486 4848 y(other) 43 b(hand,) f(the) h(consecutiv) m(e) h (p) s(oin) m(ts) e(of) h(the) g(map) g(do) g(not) g(de\014ne) f(closed) p Fn 1941 5847 a(cchv-r5.tex;) g(27/09/2001;) g(9:54;) e(p.6) p 90 rotate dyy eop %%Page: 7 7 7 6 bop Fv 3230 100 a(7) 486 291 y(curv) m(es) 28 b(around) f(the) i (\014xed) e(p) s(oin) m(t,) h(the) g(motion) g(is) f(not) i(b) s (ounded) d(close) i(the) h(the) 486 399 y(\014xed) g(p) s(oin) m(t,) h (and) g(in) f(this) g(case) i(the) g(p) s(erio) s(dic) d(orbit) h(is) h (unstable.) p Fo 788 748 a(3.) 74 b(Stabilit) m(y) 34 b(of) h(Sun-Jupiter-Asteroid) g(resonances) p Fv 486 976 a(3.1.) p Fj 65 w(Interior) e(resonances) p Fv 486 1179 a(W) -8 b(e) 27 b(consider) e(the) h(three) g(b) s(o) s(dy) f (problem) f(comp) s(osed) i(b) m(y) g(the) g(Sun) f(\() p Fm(S) p Fv 5 w(\),) i(Jupiter) 486 1287 y(\() p Fm(J) p Fv 9 w(\)) f(and) f(an) h(asteroid) g(\() p Fm(A) p Fv(\),) g(whic) m (h) f(mo) m(v) m(es) i(in) d(the) i(region) g(in) m(terior) e(to) j (the) f(orbit) 486 1395 y(of) 39 b(Jupiter.) e(F) -8 b(amilies) 38 b(of) h(p) s(erio) s(dic) d(orbits) i(in) g(the) h (PCR3BP) g(are) g(generated) 486 1503 y(as) 33 b(the) h(eccen) m (tricit) m(y) h(is) d(v) -5 b(aried.) 33 b(W) -8 b(e) 34 b(sho) m(w) m(ed) g(in) p Fk 32 w(x) p Fv(2) h(that) f(for) f(eac) m(h) i(frequency) p Fm 486 1611 a(p=q) p Fv 31 w(there) 28 b(exist) g(t) m(w) m(o) i(families) c(dep) s(ending) f(on) j(the) h (initial) c(MC.) k(The) e(stabilit) m(y) 486 1719 y(c) m(haracter) 32 b(c) m(hanges) g(as) p Fm 31 w(p=q) p Fv 34 w(is) e(v) -5 b(aried) 30 b(and) h(the) g(eccen) m(tricit) m(y) h(is) e(increased.) h (In) 486 1826 y(what) f(follo) m(ws) g(w) m(e) h(\014x) p Fm 30 w(\026) p Fv 31 w(equal) f(to) h(the) g(mass) g(of) g(Jupiter,) e (i.e.) p Fm 31 w(\026) p Fv 25 w(=) d(0) p Fm(:) p Fv(0009552.) 486 1934 y(Moreo) m(v) m(er,) k(w) m(e) f(analyze) g(all) e(resonances) h (with) f(2) p Fk 26 w(\024) p Fm 25 w(p) p Fk 25 w(\024) p Fv 25 w(9) i(and) e(1) p Fk 26 w(\024) p Fm 25 w(q) p Fk 28 w(\024) p Fv 25 w(5) i(and) 486 2042 y(w) m(e) h(add) g(the) h (further) e(constrain) m(t) h(that) h(4) p Fm(=) p Fv(3) p Fk 27 w(\024) p Fm 25 w(p=q) p Fk 28 w(\024) p Fv 25 w(5.) 602 2150 y(F) -8 b(or) 38 b(eac) m(h) h(of) e(the) h(t) m(w) m(o) h(families) c(of) j(p) s(erio) s(dic) d(orbits) h(with) g(frequency) p Fm 37 w(p=q) p Fv 486 2258 a(w) m(e) h(compute) g(the) g(linear) e (stabilit) m(y) g(through) h(the) h(trace) h(of) f(the) g(mono) s(drom) m(y) 486 2366 y(matrix) j(pro) 5 b(jected) 41 b(on) f(the) h(P) m (oincar) m(\023) -43 b(e) 43 b(surface) d(of) h(section,) g(as) g (explained) e(in) 486 2474 y(subsection) 30 b(2.4.) i(The) f(linear) e (stabilit) m(y) h(is) h(analyzed) g(with) e(resp) s(ect) j(to) g(the) f (a) m(v-) 486 2582 y(erage) e(eccen) m(tricit) m(y) g(de\014ned) d(in) h (Eq.) h(2.) h(Mark) m(ed) f(di\013erences) f(can) i(b) s(e) e(observ) m (ed) 486 2690 y(as) j(a) h(function) e(of) i(the) f(frequency) p Fm 30 w(p=q) p Fv 3 w(.) 602 2798 y(Let) 36 b(us) g(examine) g(in) f (more) h(detail) f(the) h(stabilit) m(y) f(results.) g(The) h(t) m(w) m (o) i(fami-) 486 2906 y(lies) d(asso) s(ciated) j(to) p Fm 37 w(n=n) p Fl 1361 2873 a(0) p Fv 1420 2906 a(=) e(2) p Fm(=) p Fv(1,) j(4/1,) f(3/2,) g(5/2,) h(7/2,) f(9/2) h(sho) m(w) d(a) i (similar) 486 3014 y(b) s(eha) m(viour,) 27 b(since) h(one) h(p) s (erio) s(dic) d(orbit) i(\(the) h(one) g(denoted) g(I) g(p.o.) g(in) e (T) -8 b(able) 29 b(I) s(I\)) 486 3122 y(is) 38 b(stable,) i(while) e (the) i(other) g(\(I) s(I) f(p.o.\)) h(is) f(unstable.) g(This) f(kind) f(of) j(result) f(is) 486 3230 y(observ) m(ed) 30 b(for) g(all) f(v) -5 b(alues) 30 b(of) h(the) f(a) m(v) m(erage) j(eccen) m(tricit) m(y) -8 b(.) 602 3337 y(The) 40 b(opp) s(osite) g(b) s(eha) m(viour) g(is) g (observ) m(ed) h(for) f(the) h(3/1) h(and) f(5/1) h(families,) 486 3445 y(where) h(I) g(p.o.) h(is) f(unstable,) g(while) e(I) s(I) i (p.o.) h(is) f(stable.) h(W) -8 b(e) 45 b(remark) e(that) h(in) 486 3553 y(some) 31 b(cases) g(w) m(e) g(noticed) g(v) m(ery) g(small) e (regions) h(of) h(the) g(eccen) m(tricit) m(y) h(where) e(the) 486 3661 y(stabilit) m(y) 21 b(c) m(haracter) j(w) m(as) f(the) g(opp) s (osite) f(of) h(the) f(o) m(v) m(erall) h(b) s(eha) m(viour) f(observ) m (ed) g(in) 486 3769 y(the) 31 b(in) m(terv) -5 b(al) p Fm 31 w(e) p Fk 27 w(2) p Fv 27 w(\(0) p Fm(;) p Fv 15 w(1\).) 34 b(In) c(particular) g(w) m(e) i(refer) f(to) h(the) g (families) e(asso) s(ciated) 486 3877 y(to) p Fm 40 w(p=q) p Fv 44 w(=) 41 b(5) p Fm(=) p Fv(1,) g(where) e(a) i(small) d(region) h (of) h(stabilit) m(y) f(w) m(as) h(found) e(for) i(I) g(p.o.) 486 3985 y(for) p Fm 34 w(e) p Fk 32 w(2) p Fv 31 w(\(0) p Fm(:) p Fv(766) p Fm(;) p Fv 15 w(0) p Fm(:) p Fv(787\),) g(while) 32 b(instabilit) m(y) g(w) m(as) j(observ) m(ed) f(for) h(I) s(I) e(p.o.) i (in) e(the) 486 4093 y(in) m(terv) -5 b(al) p Fm 29 w(e) p Fk 26 w(2) p Fv 25 w(\(0) p Fm(:) p Fv(769) p Fm(;) p Fv 15 w(0) p Fm(:) p Fv(778\).) 602 4201 y(As) 27 b(w) m(e) g(study) f (higher) f(order) i(resonances,) g(with) p Fm 26 w(q) p Fk 28 w(\025) p Fv 25 w(3,) g(the) g(analysis) f(of) h(the) 486 4309 y(stabilit) m(y) h(b) s(ecomes) i(m) m(uc) m(h) g(more) g (complicated) g(and) f(stable) h(regions) f(alternate) 486 4417 y(with) 22 b(unstable) g(regions) h(as) g(the) h(eccen) m(tricit) m (y) g(is) f(v) -5 b(aried.) 23 b(In) f(Figure) h(1) h(w) m(e) g(rep) s (ort) 486 4525 y(a) j(sc) m(hematic) h(picture) e(of) h(the) g (stabilit) m(y) f(c) m(haracter) j(of) e(the) g(families) e(of) j(p) s (erio) s(dic) 486 4633 y(orbits) 37 b(with) g(resonance) j(4/3,) g (5/3,) g(7/3,) g(8/3,) g(7/4,) g(9/4,) g(7/5,) g(8/5,) h(9/5.) f(In) 486 4741 y(Figure) 33 b(1,) p Fm 34 w(S) p Fv 39 w(stands) g(for) g(stable) h(motion,) p Fm 33 w(U) p Fv 44 w(for) f(unstable) g(motion) g(and) p Fm 33 w(N) 10 b(D) p Fv 486 4848 a(for) 26 b(the) h(fact) g(that) p Ff 28 w(no) f(data) p Fv 28 w(w) m(ere) h(a) m(v) -5 b(ailable,) 26 b(in) f(the) i(sense) g(that) g(the) g(computer) p Fn 1941 5847 a(cchv-r5.tex;) 42 b(27/09/2001;) g(9:54;) e(p.7) p 90 rotate dyy eop %%Page: 8 8 8 7 bop Fv 486 100 a(8) p Fr 1467 259 a(T) -6 b(able) 57 b(I) r(I) r(I.) 38 b(Appro) n(ximate) 1467 350 y(eccen) n(tricit) n(y) 69 b(leading) g(to) 1467 441 y(collision) p 1467 519 827 4 v 1517 617 a(resonance) p Fq 301 w(e) p Fc 2178 625 a(c) p 1467 682 V Fr 1517 779 a(4/3) 476 b(0.21) 1517 888 y(5/3) g(0.41) 1517 997 y(7/3) g(0.76) 1517 1106 y(8/3) g(0.92) 1517 1216 y(7/4) g(0.45) 1517 1325 y(9/4) g(0.72) 1517 1434 y(7/5) g(0.25) 1517 1543 y(8/5) g(0.37) 1517 1652 y(9/5) g(0.48) p 1467 1716 V Fv 486 2119 a(program) 28 b(w) m(as) h(not) g(able) f(to) i(\014nd) d(the) i(p) s(erio) s(dic) d (orbit) h(within) f(the) j(preassigned) 486 2227 y(accuracy) 34 b(\(10) p Fl 990 2194 a(\000) p Fh(12) p Fv 1120 2227 a(\).) g(In) e(most) h(cases,) h(the) p Fm 33 w(N) 10 b(D) p Fv 36 w(regions) 32 b(can) h(b) s(e) f(explained) f(b) m(y) 486 2335 y(in) m(v) m(oking) 37 b(close) h(encoun) m(ters) h(with) e (Jupiter.) f(An) i(appro) m(ximate) g(v) -5 b(alue) 38 b(of) g(the) 486 2443 y(eccen) m(tricit) m(y) i(leading) e(to) i (collision) d(is) h(pro) m(vided) g(in) g(T) -8 b(able) 38 b(I) s(I) s(I) g(according) h(to) 486 2551 y(Eq.) 30 b(1.) 602 2659 y(A) d(diagram) f(sho) m(wing) g(the) h(trace) h(of) f (the) g(mono) s(drom) m(y) f(matrix) g(of) h(the) g(P) m(oin-) 486 2767 y(car) m(\023) -43 b(e) 31 b(mapping) e(v) m(ersus) g(the) i(mean) f(motion) f(ratio) p Fm 31 w(n=n) p Fl 2403 2734 a(0) p Fv 2455 2767 a(is) g(rep) s(orted) h(in) f(Figure) 486 2875 y(2) 41 b(for) f(v) -5 b(arious) 40 b(v) -5 b(alues) 40 b(of) h(the) h(a) m(v) m(erage) h(eccen) m(tricit) m(y) -8 b(.) 43 b(W) -8 b(e) 42 b(remark) e(that) i(the) 486 2983 y(v) -5 b(alues) 29 b(of) i(the) f(trace) i(tend) e(to) h (\015atten) g(to) g(2) g(as) p Fm 30 w(n=n) p Fl 2303 2950 a(0) p Fv 2357 2983 a(gets) g(larger.) 486 3230 y(3.2.) p Fj 65 w(Exterior) i(resonances) p Fv 486 3445 a(In) 38 b(the) i(framew) m(ork) f(of) h(the) g(PCR3BP) -8 b(,) 40 b(w) m(e) g(consider) e(the) i(Sun) d(\() p Fm(S) p Fv 5 w(\),) k(Jupiter) 486 3553 y(\() p Fm(J) p Fv 9 w(\)) 30 b(and) f(a) h(small) e(b) s(o) s(dy) g(\() p Fm(A) p Fv(\)) j(mo) m(ving) e(outside) g(the) h(circular) e(orbit) h (de\014ned) f(b) m(y) 486 3661 y(Jupiter.) g(W) -8 b(e) 32 b(\014x) p Fm 30 w(\026) p Fv 25 w(=) 25 b(0) p Fm(:) p Fv(0009552.) 602 3769 y(Exterior) 35 b(resonances) i(are) f(c) m (haracterized) i(b) m(y) e(a) g(mean) h(motion) e(ratio) i(less) 486 3877 y(than) 24 b(1;) i(in) d(particular,) h(w) m(e) h(study) f(the) h (families) e(of) i(p) s(erio) s(dic) e(orbits) h(asso) s(ciated) 486 3985 y(to) p Fm 26 w(p=q) p Fv 28 w(=) h(1) p Fm(=) p Fv(2,) i(1/3,) h(1/4,) f(2/3,) g(3/4.) h(MCs) d(can) h(again) g(b) s(e) f(co) s(ded) g(b) m(y) h(the) g(initial) 486 4093 y(p) s(osition) 36 b(of) i(the) h(small) d(b) s(o) s(dy) h(at) i(p) s(ericen) m(ter) f(\() p Fm(P) 13 b(C) p Fv 7 w(\)) 38 b(or) g(at) h(ap) s(o) s(cen) m(ter) g (\() p Fm(AC) p Fv 7 w(\)) 486 4201 y(and) 32 b(b) m(y) h(the) h (initial) c(con\014gurations) p Fm 32 w(S) p Fk 28 w(\000) p Fm 21 w(J) p Fk 32 w(\000) p Fm 21 w(A) p Fv 34 w(or) p Fm 33 w(A) p Fk 22 w(\000) p Fm 22 w(S) p Fk 27 w(\000) p Fm 22 w(J) p Fv 9 w(.) j(W) -8 b(e) 35 b(giv) m(e) e(in) 486 4309 y(T) -8 b(able) 30 b(IV) g(the) g(co) s(des) h(of) f(the) h(MCs.) 602 4417 y(As) k(for) g(in) m(terior) e(resonances,) j(w) m(e) f(can) h (iden) m(tify) d(t) m(w) m(o) k(families) 32 b(of) k(p) s(erio) s(dic) 486 4525 y(orbits) 29 b(according) h(to) h(the) g(v) -5 b(alues) 30 b(of) p Fm 30 w(p) p Fv 30 w(and) p Fm 30 w(p) p Fk 20 w(\000) p Fm 20 w(q) p Fv 3 w(,) g(as) h(describ) s(ed) d (in) h(T) -8 b(able) 30 b(I) s(I.) 602 4633 y(As) f(a) h(summary) e(of) i(our) f(results,) f(w) m(e) i(rep) s(ort) f(in) f(Figure) h(3) h(the) f (v) -5 b(alue) 29 b(of) h(the) 486 4741 y(trace) 24 b(as) g(a) h (function) d(of) i(the) g(mean) g(motion) p Fm 23 w(n=n) p Fl 2169 4708 a(0) p Fv 2216 4741 a(corresp) s(onding) d(to) k(the) f (ab) s(o) m(v) m(e) 486 4848 y(men) m(tioned) h(c) m(hoice) i(of) p Fm 27 w(p=q) p Fv 3 w(,) f(for) g(di\013eren) m(t) g(v) -5 b(alues) 25 b(of) i(the) f(a) m(v) m(erage) j(eccen) m(tricit) m(y) -8 b(.) p Fn 1941 5847 a(cchv-r5.tex;) 42 b(27/09/2001;) g(9:54;) e(p.8) p 90 rotate dyy eop %%Page: 9 9 9 8 bop Fv 3230 100 a(9) 486 5176 y @beginspecial -21 @llx 15 @lly 548 @urx 720 @ury 3401 @rwi 5952 @rhi @setspecial %%BeginDocument: figure1.eps %!PS-Adobe-2.0 EPSF-1.2 %%Title: fig1.epsf %%Creator: Canvas 3.5 %%For: Alessandra Celletti %%CreationDate: Ven, 3 ago 2001 23:13 %%BoundingBox: -21 15 548 720 %%DocumentProcSets: CanvasDict %%DocumentSuppliedProcSets: CanvasDict %%Copyright ©1988-91 Deneba Systems, Inc. - All Rights Reserved Worldwide %%DocumentFonts: Geneva %%DocumentNeededFonts: Geneva %%EndComments %%BeginProcSet:CanvasDict /CanvasDict where not{/CanvasDict 250 dict def}{pop}ifelse CanvasDict begin systemdict/setpacking known{/origpack currentpacking def true setpacking}if /bdf{bind def}bind def /_cv 20 dict begin /isDeviceColor 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f/filltype edf}{newpath}ifelse}bdf /spx{SpaceExtra 0 32 4 -1 roll widthshow}bdf /lsx{SpaceExtra 0 32 LetterSpace 0 6 -1 roll awidthshow}bdf /Rjust{stringwidth pop JustOffset exch sub /JustOffset edf}bdf /Cjust{stringwidth pop 2 div JustOffset exch sub /JustOffset edf}bdf /adjfit{stringwidth pop LetterSpace StringLength 1 sub mul add SpaceExtra NumSpaces mul add dup /pw edf JustOffset exch sub dup /wdif edf StringLength div LetterSpace add /LetterSpace edf}bdf /ulb{currentpoint pop /underlinpt edf}bdf /ule{gsave currentpoint newpath moveto currentfont dup /ft1 known{dup /ft1 get begin /FontMatrix get FontMatrix tpmx concatmatrix pop} {begin FontMatrix tpmx copy pop}ifelse currentfont /FontInfo known {FontInfo begin UnderlinePosition UnderlineThickness end}{-.1 .05}ifelse end dup tpmx dtransform pop setlinewidth dup tpmx dtransform pop 0 exch rmoveto underlinpt currentpoint pop sub 0 rlineto stroke grestore}bdf /fittext{ /SpaceExtra edf /LetterSpace edf /StringLength edf /NumSpaces edf 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def/FontType 3 def FontDirectory 3 index get /Encoding get/Encoding exch def /proc2 edf/ft2 exch findfont def/ft1 exch findfont def/FontBBox [0 0 1 1] def /BuildChar{wdict begin/chr edf/ftdt edf/chrst wrk1 dup 0 chr put def ftdt/proc2 get exec end}def end tempFT definefont pop}bdf /OLFt{dup dhOdh FontDirectory 1 index known{exch pop} {dup 3 -1 roll dup MakOF {outproc} mkFT}ifelse}bdf /mshw{moveto show}bdf /outproc{ftdt/ft1 get setfont gsave chrst sfWidth grestore setcharwidth dblsh}bdf /dblsh{currentgray 1 setgray chrst 0 0 mshw setgray ftdt/ft2 get setfont chrst 0 0 mshw}bdf /ShadChar{ftdt/ft1 get setfont gsave chrst sfWidth 1 index 0 ne{exch .05 add exch}if grestore setcharwidth chrst .06 0 mshw 0 .05 translate dblsh}bdf /ShFt{dup dhSdh FontDirectory 1 index known{exch pop} {dup 3 -1 roll dup MakOF {ShadChar} mkFT}ifelse}bdf /LswUnits{72 75 div dup scale}bdf /erasefill{_bp}def /CVvec 256 array def /NUL/SOH/STX/ETX/EOT/ENQ/ACK/BEL/BS/HT/LF/VT/FF/CR/SO/SI/DLE/DC1/DC2/DC3/DC4/NAK/SYN/ETB/CAN/EM/SUB/ESC/FS/GS/RS/US CVvec 0 32 getinterval astore pop CVvec 32/Times-Roman findfont/Encoding get 32 96 getinterval putinterval CVvec dup 39/quotesingle put 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/blank/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand/Acircumflex/Ecircumflex/Aacute /Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave/Oacute/Ocircumflex /apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron CVvec 128 128 getinterval astore pop end %%EndProcSet %%BeginSetup CanvasDict begin 0 setlinecap 0 setlinejoin 4 setmiterlimit /currot 0 def origmtx currentmatrix pop [] 0 setdash 1 1 setpen 1 fg 0 pg 0 frg 1 bkg newpath /dbg F def %%EndSetup % ---- Object #1:331 Obj Type: 99 % ---- Object #2:33 Obj Type: 99 % ---- Object #3:5 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 52 651 moveto 265 651 lineto F dostroke grestore % ---- Object #4:8 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 11.375 658 moveto (4) show restore % ---- Object #5:10 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 13 653 moveto 25 653 lineto F dostroke grestore % ---- Object #6:9 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 12.375 632 moveto (3) show restore % ---- Object #7:11 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 52 655 moveto 52 647 lineto F dostroke grestore % ---- Object #8:12 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 152 654 moveto 152 646 lineto F dostroke grestore % ---- Object #9:13 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 142 654 moveto 142 646 lineto F dostroke grestore % ---- Object #10:14 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 82 654 moveto 82 646 lineto F dostroke grestore % ---- Object #11:15 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 266 655 moveto 266 647 lineto F dostroke grestore % ---- Object #12:17 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath -19 424 moveto -19 424 lineto F dostroke grestore % ---- Object #13:19 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 223 655 moveto 223 647 lineto F dostroke grestore % ---- Object #14:20 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 48.375 631.5 moveto (0) show restore % ---- Object #15:6 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 262.375 631.5 moveto (1) show restore % ---- Object #16:21 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 73.375 631.5 moveto (0.1) F F 17.6377 0 3 0.3188 0 fittext restore % ---- Object #17:22 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 116.375 631.5 moveto (0.49) F F 24.9727 0 4 0.3242 0 fittext restore % ---- Object #18:23 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 147.375 631.5 moveto (0.502) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #19:24 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 207.375 631.5 moveto (0.794) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #20:25 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 180.375 660 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #21:26 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 243.375 660 moveto (S) show restore % ---- Object #22:27 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 183.375 145.5 moveto (U) show restore % ---- Object #23:29 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 170.375 363.75 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #24:30 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 363.375 363.5 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #25:31 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 439.375 292.5 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #26:32 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 59.375 660 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #27:34 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 103.375 660 moveto (S) show restore % ---- Object #28:35 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 151.375 581 moveto (U) show restore % ---- Object #29:36 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 483.375 218.25 moveto (U) show restore % ---- Object #30:37 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 142.375 660 moveto (U) show restore % ---- Object #31:38 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 223.375 145.5 moveto (U) show restore % ---- Object #32:7 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 104.375 696 moveto (I o.p.) F F 55.4775 1 6 0 5.4775 fittext restore % ---- Object #33:39 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 374.375 695 moveto (II o.p.) F F 64.8682 1 7 0 7.8682 fittext restore % ---- Object #34:40 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 314 650 moveto 527 650 lineto F dostroke grestore % ---- Object #35:44 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 314 654 moveto 314 646 lineto F dostroke grestore % ---- Object #36:47 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 378 653 moveto 378 645 lineto F dostroke grestore % ---- Object #37:48 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 528 654 moveto 528 646 lineto F dostroke grestore % ---- Object #38:49 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 409 653 moveto 409 645 lineto F dostroke grestore % ---- Object #39:50 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 310.375 630.75 moveto (0) show restore % ---- Object #40:51 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 524.375 630.75 moveto (1) show restore % ---- Object #41:57 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 150.375 437 moveto (S) show restore % ---- Object #42:58 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 336.375 658 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #43:59 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 388.375 658 moveto (S) show restore % ---- Object #44:60 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 452.375 658 moveto (U) show restore % ---- Object #45:28 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 456.375 218.25 moveto (S) show restore % ---- Object #46:41 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 204.375 145.5 moveto (S) show restore % ---- Object #47:42 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 107.375 145.5 moveto (S) show restore % ---- Object #48:43 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 160.375 145.5 moveto (S) show restore % ---- Object #49:45 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 358.375 630.75 moveto (0.265) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #50:18 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 402.375 630.75 moveto (0.4) F F 17.6377 0 3 0.3188 0 fittext restore % ---- Object #51:52 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 52 574 moveto 265 574 lineto F dostroke grestore % ---- Object #52:53 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 10.375 582 moveto (5) show restore % ---- Object #53:54 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 12 577 moveto 24 577 lineto F dostroke grestore % ---- Object #54:55 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 11.375 558 moveto (3) show restore % ---- Object #55:56 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 52 578 moveto 52 570 lineto F dostroke grestore % ---- Object #56:62 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 143 578 moveto 143 570 lineto F dostroke grestore % ---- Object #57:63 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 82 577 moveto 82 569 lineto F dostroke grestore % ---- Object #58:64 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 266 578 moveto 266 570 lineto F dostroke grestore % ---- Object #59:65 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 163 578 moveto 163 570 lineto F dostroke grestore % ---- Object #60:66 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 48.375 555.5 moveto (0) show restore % ---- Object #61:67 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 262.375 555.5 moveto (1) show restore % ---- Object #62:72 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 475.375 580.5 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #63:73 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 212.375 581 moveto (S) show restore % ---- Object #64:74 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 100.375 581 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #65:75 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 483.375 363.5 moveto (S) show restore % ---- Object #66:76 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 60.375 581 moveto (U) show restore % ---- Object #67:77 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 314 573 moveto 527 573 lineto F dostroke grestore % ---- Object #68:78 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 314 577 moveto 314 569 lineto F dostroke grestore % ---- Object #69:79 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 355 576.5 moveto 355 568.5 lineto F dostroke grestore % ---- Object #70:80 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 528 577 moveto 528 569 lineto F dostroke grestore % ---- Object #71:81 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 420 576.5 moveto 420 568.5 lineto F dostroke grestore % ---- Object #72:82 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 310.375 555.25 moveto (0) show restore % ---- Object #73:83 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 524.375 555.25 moveto (1) show restore % ---- Object #74:84 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 336.375 580.5 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #75:85 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 388.375 580.5 moveto (S) show restore % ---- Object #76:86 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 431.375 580.5 moveto (U) show restore % ---- Object #77:61 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 448 576.5 moveto 448 568.5 lineto F dostroke grestore % ---- Object #78:68 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 64.375 555.5 moveto (0.252) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #79:46 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 117.375 555.5 moveto (0.455) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #80:69 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 154.375 555.5 moveto (0.56) F F 24.9727 0 4 0.3242 0 fittext restore % ---- Object #81:87 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 344.375 555.25 moveto (0.2) F F 17.6377 0 3 0.3188 0 fittext restore % ---- Object #82:70 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 396.375 555.25 moveto (0.584) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #83:88 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 440.375 554.25 moveto (0.613) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #84:90 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 462.375 435 moveto (U) show restore % ---- Object #85:91 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 52 502 moveto 265 502 lineto F dostroke grestore % ---- Object #86:92 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 10.375 510 moveto (7) show restore % ---- Object #87:93 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 12 505 moveto 24 505 lineto F dostroke grestore % ---- Object #88:94 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 11.375 486 moveto (3) show restore % ---- Object #89:95 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 52 506 moveto 52 498 lineto F dostroke grestore % ---- Object #90:96 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 249 506 moveto 249 498 lineto F dostroke grestore % ---- Object #91:98 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 266 506 moveto 266 498 lineto F dostroke grestore % ---- Object #92:99 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 163 506 moveto 163 498 lineto F dostroke grestore % ---- Object #93:100 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 48.375 483.75 moveto (0) show restore % ---- Object #94:101 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 262.375 483.75 moveto (1) show restore % ---- Object #95:102 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 253.375 508.5 moveto (S) show restore % ---- Object #96:103 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 179.375 508.5 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #97:104 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 93.375 508.5 moveto (U) show restore % ---- Object #98:105 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 314 501 moveto 527 501 lineto F dostroke grestore % ---- Object #99:106 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 314 505 moveto 314 497 lineto F dostroke grestore % ---- Object #100:108 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 528 505 moveto 528 497 lineto F dostroke grestore % ---- Object #101:109 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 500 504.5 moveto 500 496.5 lineto F dostroke grestore % ---- Object #102:110 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 310.375 483.5 moveto (0) show restore % ---- Object #103:111 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 524.375 483.5 moveto (1) show restore % ---- Object #104:112 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 506.375 508 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #105:113 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 388.375 508 moveto (S) show restore % ---- Object #106:114 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 484.375 508 moveto (U) show restore % ---- Object #107:115 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 481 504.5 moveto 481 496.5 lineto F dostroke grestore % ---- Object #108:97 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 149.375 483.75 moveto (0.62) F F 24.9727 0 4 0.3242 0 fittext restore % ---- Object #109:89 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 235.375 483.75 moveto (0.9) F F 17.6377 0 3 0.3188 0 fittext restore % ---- Object #110:117 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 447.375 483.5 moveto (0.808) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #111:107 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 486.375 483.5 moveto (0.855) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #112:118 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 50 430 moveto 263 430 lineto F dostroke grestore % ---- Object #113:119 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 8.375 438 moveto (8) show restore % ---- Object #114:120 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 10 433 moveto 22 433 lineto F dostroke grestore % ---- Object #115:121 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 9.375 414 moveto (3) show restore % ---- Object #116:122 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 50 434 moveto 50 426 lineto F dostroke grestore % ---- Object #117:124 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 264 434 moveto 264 426 lineto F dostroke grestore % ---- Object #118:126 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 46.375 411.75 moveto (0) show restore % ---- Object #119:127 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 260.375 411.75 moveto (1) show restore % ---- Object #120:128 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 245.375 363.75 moveto (S) show restore % ---- Object #121:129 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 496.375 435 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #122:130 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 108.375 363.75 moveto (U) show restore % ---- Object #123:131 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 312 429 moveto 525 429 lineto F dostroke grestore % ---- Object #124:132 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 312 433 moveto 312 425 lineto F dostroke grestore % ---- Object #125:133 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 526 433 moveto 526 425 lineto F dostroke grestore % ---- Object #126:134 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 481 431.5 moveto 481 423.5 lineto F dostroke grestore % ---- Object #127:135 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 308.375 409.25 moveto (0) show restore % ---- Object #128:136 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 522.375 411.25 moveto (1) show restore % ---- Object #129:137 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 423.375 435 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #130:138 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 397.375 435 moveto (S) show restore % ---- Object #131:139 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 342.375 435 moveto (U) show restore % ---- Object #132:140 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 447 432.5 moveto 447 424.5 lineto F dostroke grestore % ---- Object #133:125 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 387 433 moveto 387 425 lineto F dostroke grestore % ---- Object #134:141 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 413 433 moveto 413 425 lineto F dostroke grestore % ---- Object #135:143 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 356.375 411.25 moveto (0.463) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #136:116 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 396.375 411.25 moveto (0.484) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #137:123 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 434.375 411.25 moveto (0.583) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #138:142 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 472.375 411.25 moveto (0.746) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #139:145 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 66.375 363.75 moveto 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lineto F dostroke grestore % ---- Object #146:152 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 265 364 moveto 265 356 lineto F dostroke grestore % ---- Object #147:153 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 47.375 343 moveto (0) show restore % ---- Object #148:154 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 261.375 343 moveto (1) show restore % ---- Object #149:155 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 502.375 363.5 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #150:156 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 313 359 moveto 526 359 lineto F dostroke grestore % ---- Object #151:157 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 313 363 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51 292 moveto 51 284 lineto F dostroke grestore % ---- Object #180:187 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 191 291 moveto 191 283 lineto F dostroke grestore % ---- Object #181:188 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 265 292 moveto 265 284 lineto F dostroke grestore % ---- Object #182:189 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 162 292 moveto 162 284 lineto F dostroke grestore % ---- Object #183:190 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 47.375 270.5 moveto (0) show restore % ---- Object #184:191 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 261.375 270.5 moveto (1) show restore % ---- Object #185:192 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 107.375 291.5 moveto (S) show restore % ---- Object #186:193 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 224.375 291.5 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #187:194 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 169.375 291.5 moveto (U) show restore % ---- Object #188:195 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 313 287 moveto 526 287 lineto F dostroke grestore % ---- Object #189:196 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 313 291 moveto 313 283 lineto F dostroke grestore % ---- Object #190:197 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 527 291 moveto 527 283 lineto F dostroke grestore % ---- Object #191:198 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 499 290.5 moveto 499 282.5 lineto F dostroke grestore % ---- Object #192:199 Obj Type: 2 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0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 393.375 269.5 moveto (0.486) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #203:206 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 449.375 269.5 moveto (0.894) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #204:208 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 487.375 269.5 moveto (0.945) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #205:211 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 48 212 moveto 261 212 lineto F dostroke grestore % ---- Object #206:212 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 10.375 220 moveto (7) show restore % ---- Object #207:213 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 12 215 moveto 24 215 lineto F dostroke grestore % ---- Object #208:214 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 11.375 196 moveto (5) show restore % ---- Object #209:215 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 48 216 moveto 48 208 lineto F dostroke grestore % ---- Object #210:216 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 188 215 moveto 188 207 lineto F dostroke grestore % ---- Object #211:217 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 262 216 moveto 262 208 lineto F dostroke grestore % ---- Object #212:218 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 159 216 moveto 159 208 lineto F dostroke grestore % ---- Object #213:219 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 44.375 195.25 moveto (0) show restore % ---- Object #214:220 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 258.375 195.25 moveto (1) show restore % ---- Object #215:221 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 169.375 216.5 moveto (S) show restore % ---- Object #216:222 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 221.375 216.5 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #217:223 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 117.375 216.5 moveto (U) show restore % ---- Object #218:224 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 310 211 moveto 523 211 lineto F dostroke grestore % ---- Object #219:225 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 310 215 moveto 310 207 lineto F dostroke grestore % ---- Object #220:226 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 524 215 moveto 524 207 lineto F dostroke grestore % ---- Object #221:227 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 496 214.5 moveto 496 206.5 lineto F dostroke grestore % ---- Object #222:228 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 306.375 194.5 moveto (0) show restore % ---- Object #223:229 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 520.375 194.5 moveto (1) show restore % ---- Object #224:230 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 502.375 218.25 moveto (ND) F F 15.0898 0 2 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setlinejoin gsave newpath 92 216 moveto 92 208 lineto F dostroke grestore % ---- Object #232:235 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 70.375 195.25 moveto (0.308) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #233:210 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 142.375 195.25 moveto (0.52) F F 24.9727 0 4 0.3242 0 fittext restore % ---- Object #234:234 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 185.375 195.25 moveto (0.612) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #235:240 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 317.375 194.5 moveto (0.083) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #236:241 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 353.375 194.5 moveto (0.095) F F 32.3076 0 5 0.3269 0 fittext restore % ---- Object #237:242 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 418.375 194.75 moveto (0.73) F F 24.9727 0 4 0.3242 0 fittext restore % ---- Object #238:243 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 454.375 194.5 moveto (0.82) F F 24.9727 0 4 0.3242 0 fittext restore % ---- Object #239:244 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 488.375 194.5 moveto (0.87) F F 24.9727 0 4 0.3242 0 fittext restore % ---- Object #240:246 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 63.375 216.5 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #241:248 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 385.375 218.25 moveto (ND) F F 15.0898 0 2 -0.9102 0 fittext restore % ---- Object #242:249 Obj Type: 2 save 0 setgray mark /|___Geneva /Geneva T cvRecFont 12 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 408.375 144.75 moveto (U) show restore % ---- Object #243:251 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 49 140 moveto 262 140 lineto F dostroke grestore % ---- Object #244:252 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 11.375 148 moveto (8) show restore % ---- Object #245:253 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 13 143 moveto 25 143 lineto F dostroke grestore % ---- Object #246:254 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 18 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 12.375 124 moveto (5) show restore % ---- Object #247:255 Obj Type: 3 1 1 setpen 2 setlinecap 0 setlinejoin gsave newpath 49 144 moveto 49 136 lineto F dostroke grestore % ---- Object #248:256 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 176 143 moveto 176 135 lineto F dostroke grestore % ---- Object #249:257 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 263 144 moveto 263 136 lineto F dostroke grestore % ---- Object #250:258 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 153 144 moveto 153 136 lineto F dostroke grestore % ---- Object #251:259 Obj Type: 2 0 0 setpen save 0 setgray mark /|___Geneva /Geneva T cvRecFont 10 fts /|___Geneva findfont exch scalefont setfont 0 setgray 0 setgray 45.375 122.75 moveto (0) show restore % ---- Object #252:260 Obj Type: 2 save 0 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Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1075.5 1781.5 moveto 1078.5 1784.5 lineto F dostroke grestore % ---- Object #280:429 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1075.5 1781.5 moveto 1075.5 1784.5 lineto F dostroke grestore % ---- Object #281:430 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1075.5 1781.5 moveto 1075.5 1778.5 lineto F dostroke grestore % ---- Object #282:431 Obj Type: 2 save 0 setgray mark /|___Arial-BoldMT /Arial-BoldMT T cvRecFont 24 fts /|___Arial-BoldMT findfont exch scalefont setfont 0 setgray 0 setgray 705.375 2021 moveto (e = 0.2) F F 74.0625 2 7 0 0 fittext restore % ---- Object #283:432 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 404.375 1643 moveto (-4) F F 12.4482 0 2 0 0 fittext restore % ---- Object #284:433 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 404.375 1687 moveto (-2) F F 12.4482 0 2 0 0 fittext restore % ---- Object #285:434 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 407.375 1731 moveto (0) show restore % ---- Object #286:435 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 407.375 1775 moveto (2) show restore % ---- Object #287:436 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 407.375 1819 moveto (4) show restore % ---- Object #288:437 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 407.375 1864 moveto (6) show restore % ---- Object #289:438 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 407.375 1908 moveto (8) show restore % ---- Object #290:439 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 401.375 1952 moveto (10) F F 15.5723 0 2 0 0 fittext restore % ---- Object #291:440 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 401.375 1996 moveto (12) F F 15.5723 0 2 0 0 fittext restore % ---- Object #292:441 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 10 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 418.375 1721 moveto (1) show restore % ---- Object #293:442 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 496.375 1717 moveto (1.5) F F 19.4619 0 3 0 0 fittext restore % ---- Object #294:443 Obj Type: 2 save 0 setgray mark 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1372 lineto 474 1375 lineto closepath F dostroke % ---- Object #333:634 Obj Type: 9 0 0 setpen 485 1275 moveto 488 1272 lineto 485 1269 lineto 482 1272 lineto 485 1275 lineto closepath F dofill % ---- Object #334:635 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 485 1275 moveto 488 1272 lineto 485 1269 lineto 482 1272 lineto 485 1275 lineto closepath F dostroke % ---- Object #335:636 Obj Type: 9 0 0 setpen 502 1412 moveto 505 1409 lineto 502 1406 lineto 499 1409 lineto 502 1412 lineto closepath F dofill % ---- Object #336:637 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 502 1412 moveto 505 1409 lineto 502 1406 lineto 499 1409 lineto 502 1412 lineto closepath F dostroke % ---- Object #337:638 Obj Type: 9 0 0 setpen 542 1329 moveto 545 1326 lineto 542 1323 lineto 539 1326 lineto 542 1329 lineto closepath F dofill % ---- Object #338:639 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 542 1329 moveto 545 1326 lineto 542 1323 lineto 539 1326 lineto 542 1329 lineto closepath F dostroke % ---- Object #339:640 Obj Type: 9 0 0 setpen 583 1419 moveto 586 1416 lineto 583 1413 lineto 580 1416 lineto 583 1419 lineto closepath F dofill % ---- Object #340:641 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 583 1419 moveto 586 1416 lineto 583 1413 lineto 580 1416 lineto 583 1419 lineto closepath F dostroke % ---- Object #341:642 Obj Type: 9 0 0 setpen 624 1390 moveto 627 1387 lineto 624 1384 lineto 621 1387 lineto 624 1390 lineto closepath F dofill % ---- Object #342:643 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 624 1390 moveto 627 1387 lineto 624 1384 lineto 621 1387 lineto 624 1390 lineto closepath F dostroke % ---- Object #343:644 Obj Type: 9 0 0 setpen 638 1453 moveto 641 1450 lineto 638 1447 lineto 635 1450 lineto 638 1453 lineto closepath F dofill % ---- Object #344:645 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 638 1453 moveto 641 1450 lineto 638 1447 lineto 635 1450 lineto 638 1453 lineto closepath F dostroke % ---- Object #345:646 Obj Type: 9 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801 1413 lineto 798 1416 lineto 801 1419 lineto closepath F dofill % ---- Object #352:653 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 801 1419 moveto 804 1416 lineto 801 1413 lineto 798 1416 lineto 801 1419 lineto closepath F dostroke % ---- Object #353:654 Obj Type: 9 0 0 setpen 828 1419 moveto 831 1416 lineto 828 1413 lineto 825 1416 lineto 828 1419 lineto closepath F dofill % ---- Object #354:655 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 828 1419 moveto 831 1416 lineto 828 1413 lineto 825 1416 lineto 828 1419 lineto closepath F dostroke % ---- Object #355:656 Obj Type: 9 0 0 setpen 910 1419 moveto 913 1416 lineto 910 1413 lineto 907 1416 lineto 910 1419 lineto closepath F dofill % ---- Object #356:657 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 910 1419 moveto 913 1416 lineto 910 1413 lineto 907 1416 lineto 910 1419 lineto closepath F dostroke % ---- Object #357:658 Obj Type: 9 0 0 setpen 991 1419 moveto 994 1416 lineto 991 1413 lineto 988 1416 lineto 991 1419 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0 setgray 1241.375 457 moveto (-1) F F 12.4482 0 2 0 0 fittext restore % ---- Object #1111:1417 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 1244.375 515 moveto (0) show restore % ---- Object #1112:1418 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 1244.375 573 moveto (1) show restore % ---- Object #1113:1419 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 1244.375 630 moveto (2) show restore % ---- Object #1114:1420 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 1244.375 688 moveto (3) show restore % ---- Object #1115:1421 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 10 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 1255.375 505 moveto (1) show restore % ---- Object #1116:1422 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 1333.375 501 moveto (1.5) F F 19.4619 0 3 0 0 fittext restore % ---- Object #1117:1423 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 1419.375 501 moveto (2) show restore % ---- Object #1118:1424 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 1497.375 501 moveto (2.5) F F 19.4619 0 3 0 0 fittext restore % ---- Object #1119:1425 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 1583.375 501 moveto (3) show restore % ---- Object #1120:1426 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 1661.375 501 moveto (3.5) F F 19.4619 0 3 0 0 fittext restore % ---- Object #1121:1427 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 1747.375 501 moveto (4) show restore % ---- Object #1122:1428 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 1825.375 501 moveto (4.5) F F 19.4619 0 3 0 0 fittext restore % ---- Object #1123:1429 Obj Type: 2 save 0 setgray mark /|___ArialMT /ArialMT T cvRecFont 14 fts /|___ArialMT findfont exch scalefont setfont 0 setgray 0 setgray 1911.375 501 moveto (5) show restore % ---- Object #1124:1430 Obj Type: 2 save 0 setgray mark /|___Arial-BoldMT /Arial-BoldMT T cvRecFont 18 fts /|___Arial-BoldMT findfont exch scalefont setfont 0 setgray 0 setgray 1576.375 345 moveto (n/n') F F 31.2715 0 4 0 0 fittext restore % ---- Object #1125:764 Obj Type: 99 % ---- Object #1126:457 Obj Type: 9 0 0 setpen 1 fg 1 bkg 1262 1987 moveto 1918 1987 lineto 1918 1641 lineto 1262 1641 lineto 1262 1987 lineto closepath F dofill % ---- Object #1127:458 Obj Type: 3 0.0039 0.0039 setpen 2 setlinecap 0 setlinejoin gsave newpath 1261.5039 1987.4961 moveto 1261.5039 1641.4961 lineto F dostroke grestore % ---- Object #1128:459 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1258.5039 1641.4961 moveto 1261.5039 1641.4961 lineto F dostroke grestore % ---- Object #1129:460 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1258.5039 1684.4961 moveto 1261.5039 1684.4961 lineto F dostroke grestore % ---- Object #1130:461 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1258.5039 1727.4961 moveto 1261.5039 1727.4961 lineto F dostroke grestore % ---- Object #1131:462 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1258.5039 1771.4961 moveto 1261.5039 1771.4961 lineto F dostroke grestore % ---- Object #1132:463 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1258.5039 1814.4961 moveto 1261.5039 1814.4961 lineto F dostroke grestore % ---- Object #1133:464 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1258.5039 1857.4961 moveto 1261.5039 1857.4961 lineto F dostroke grestore % ---- Object #1134:465 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1258.5039 1900.4961 moveto 1261.5039 1900.4961 lineto F dostroke grestore % ---- Object #1135:466 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1258.5039 1944.4961 moveto 1261.5039 1944.4961 lineto F dostroke grestore % ---- Object #1136:467 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1258.5039 1987.4961 moveto 1261.5039 1987.4961 lineto F dostroke grestore % ---- Object #1137:468 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1261.5039 1814.4961 moveto 1917.5039 1814.4961 lineto F dostroke grestore % ---- Object #1138:469 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1261.5039 1811.4961 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setlinecap 0 setlinejoin gsave newpath 1835.5039 1811.4961 moveto 1835.5039 1814.4961 lineto F dostroke grestore % ---- Object #1146:477 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1917.5039 1811.4961 moveto 1917.5039 1814.4961 lineto F dostroke grestore % ---- Object #1147:478 Obj Type: 9 0 setlinecap 0 setlinejoin [10 4] 0 setdash 1262.002 1726.998 moveto 1317.002 1726.998 lineto 1344.002 1726.998 lineto 1360.002 1726.998 lineto 1372.002 1726.998 lineto 1385.002 1726.998 lineto 1393.002 1726.998 lineto 1426.002 1726.998 lineto 1467.002 1726.998 lineto 1481.002 1726.998 lineto 1508.002 1726.998 lineto 1535.002 1726.998 lineto 1589.002 1726.998 lineto 1645.002 1726.998 lineto 1672.002 1726.998 lineto 1754.002 1726.998 lineto 1836.002 1726.998 lineto 1918.002 1726.998 lineto F dostroke % ---- Object #1148:479 Obj Type: 9 0 setlinecap 0 setlinejoin [10 4] 0 setdash 1262.002 1899.998 moveto 1317.002 1899.998 lineto 1344.002 1899.998 lineto 1360.002 1899.998 lineto 1372.002 1899.998 lineto 1385.002 1899.998 lineto 1393.002 1899.998 lineto 1426.002 1899.998 lineto 1467.002 1899.998 lineto 1481.002 1899.998 lineto 1508.002 1899.998 lineto 1535.002 1899.998 lineto 1589.002 1899.998 lineto 1645.002 1899.998 lineto 1672.002 1899.998 lineto 1754.002 1899.998 lineto 1836.002 1899.998 lineto 1918.002 1899.998 lineto F dostroke % ---- Object #1149:480 Obj Type: 9 0 0 setpen 0 fg 0 bkg 1317 1837 moveto 1320 1834 lineto 1317 1831 lineto 1314 1834 lineto 1317 1837 lineto closepath F dofill % ---- Object #1150:481 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin [] 0 setdash 1317 1837 moveto 1320 1834 lineto 1317 1831 lineto 1314 1834 lineto 1317 1837 lineto closepath F dostroke % ---- Object #1151:482 Obj Type: 9 0 0 setpen 1344 1890 moveto 1347 1887 lineto 1344 1884 lineto 1341 1887 lineto 1344 1890 lineto closepath F dofill % ---- Object #1152:483 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 1344 1890 moveto 1347 1887 lineto 1344 1884 lineto 1341 1887 lineto 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1881 lineto closepath F dostroke % ---- Object #1159:490 Obj Type: 9 0 0 setpen 1481 1924 moveto 1484 1921 lineto 1481 1918 lineto 1478 1921 lineto 1481 1924 lineto closepath F dofill % ---- Object #1160:491 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 1481 1924 moveto 1484 1921 lineto 1481 1918 lineto 1478 1921 lineto 1481 1924 lineto closepath F dostroke % ---- Object #1161:492 Obj Type: 9 0 0 setpen 1508 1898 moveto 1511 1895 lineto 1508 1892 lineto 1505 1895 lineto 1508 1898 lineto closepath F dofill % ---- Object #1162:493 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 1508 1898 moveto 1511 1895 lineto 1508 1892 lineto 1505 1895 lineto 1508 1898 lineto closepath F dostroke % ---- Object #1163:494 Obj Type: 9 0 0 setpen 1535 1900 moveto 1538 1897 lineto 1535 1894 lineto 1532 1897 lineto 1535 1900 lineto closepath F dofill % ---- Object #1164:495 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 1535 1900 moveto 1538 1897 lineto 1535 1894 lineto 1532 1897 lineto 1535 1900 lineto closepath F dostroke % ---- Object #1165:496 Obj Type: 9 0 0 setpen 1589 1905 moveto 1592 1902 lineto 1589 1899 lineto 1586 1902 lineto 1589 1905 lineto closepath F dofill % ---- Object #1166:497 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 1589 1905 moveto 1592 1902 lineto 1589 1899 lineto 1586 1902 lineto 1589 1905 lineto closepath F dostroke % ---- Object #1167:498 Obj Type: 9 0 0 setpen 1645 1903 moveto 1648 1900 lineto 1645 1897 lineto 1642 1900 lineto 1645 1903 lineto closepath F dofill % ---- Object #1168:499 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 1645 1903 moveto 1648 1900 lineto 1645 1897 lineto 1642 1900 lineto 1645 1903 lineto closepath F dostroke % ---- Object #1169:500 Obj Type: 9 0 0 setpen 1672 1903 moveto 1675 1900 lineto 1672 1897 lineto 1669 1900 lineto 1672 1903 lineto closepath F dofill % ---- Object #1170:501 Obj Type: 9 1 1 setpen 0 setlinecap 0 setlinejoin 1672 1903 moveto 1675 1900 lineto 1672 1897 lineto 1669 1900 lineto 1672 1903 lineto 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Object #1184:515 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1393.5 1679.5 moveto 1396.5 1676.5 lineto F dostroke grestore % ---- Object #1185:516 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1393.5 1679.5 moveto 1390.5 1676.5 lineto F dostroke grestore % ---- Object #1186:517 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1393.5 1679.5 moveto 1396.5 1682.5 lineto F dostroke grestore % ---- Object #1187:518 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1393.5 1679.5 moveto 1393.5 1682.5 lineto F dostroke grestore % ---- Object #1188:519 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1393.5 1679.5 moveto 1393.5 1676.5 lineto F dostroke grestore % ---- Object #1189:520 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1425.5 1950.5 moveto 1422.5 1953.5 lineto F dostroke grestore % ---- Object #1190:521 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1425.5 1950.5 moveto 1428.5 1947.5 lineto F dostroke grestore % ---- Object #1191:522 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1425.5 1950.5 moveto 1422.5 1947.5 lineto F dostroke grestore % ---- Object #1192:523 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1425.5 1950.5 moveto 1428.5 1953.5 lineto F dostroke grestore % ---- Object #1193:524 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1425.5 1950.5 moveto 1425.5 1953.5 lineto F dostroke grestore % ---- Object #1194:525 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1425.5 1950.5 moveto 1425.5 1947.5 lineto F dostroke grestore % ---- Object #1195:526 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1467.5 1928.5 moveto 1464.5 1931.5 lineto F dostroke grestore % ---- Object #1196:527 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1467.5 1928.5 moveto 1470.5 1925.5 lineto F dostroke grestore % ---- Object #1197:528 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1467.5 1928.5 moveto 1464.5 1925.5 lineto F dostroke grestore % ---- Object #1198:529 Obj Type: 3 2 setlinecap 0 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1481.5 1885.5 moveto 1481.5 1888.5 lineto F dostroke grestore % ---- Object #1206:537 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1481.5 1885.5 moveto 1481.5 1882.5 lineto F dostroke grestore % ---- Object #1207:538 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1508.5 1909.5 moveto 1505.5 1912.5 lineto F dostroke grestore % ---- Object #1208:539 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1508.5 1909.5 moveto 1511.5 1906.5 lineto F dostroke grestore % ---- Object #1209:540 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1508.5 1909.5 moveto 1505.5 1906.5 lineto F dostroke grestore % ---- Object #1210:541 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1508.5 1909.5 moveto 1511.5 1912.5 lineto F dostroke grestore % ---- Object #1211:542 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1508.5 1909.5 moveto 1508.5 1912.5 lineto F dostroke grestore % ---- Object #1212:543 Obj Type: 3 2 setlinecap 0 setlinejoin gsave newpath 1508.5 1909.5 moveto 1508.5 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i(systems) g(ha) m(v) m(e) i(b) s(een) e(disco) m(v) m (ered) h(around) e(stars) i(of) g(di\013eren) m(t) f(t) m(yp) s(es) 486 3048 y(and) d(sizes.) h(The) f(ratio) h(of) g(the) g(mass) g(of) g(the) g(planet) f(to) i(that) f(of) g(the) h(cen) m(tral) f(star) 486 3156 y(is) g(usually) f(uncertain,) h(due) g(to) i(the) g(unkno) m(wn) d (v) -5 b(alue) 27 b(of) g(the) h(planetary) e(orbital) 486 3264 y(inclination.) i(A) k(lo) m(w) m(er) g(b) s(ound) d(on) j(suc) m (h) f(v) -5 b(alue) 31 b(can) h(b) s(e) e(giv) m(en,) i(but) f(the) h (actual) 486 3372 y(mass) e(could) f(b) s(e) h(larger.) 602 3480 y(As) 36 b(a) g(consequence) h(of) f(this,) g(it) f(is) g(useful) g (to) i(examine) e(the) i(stabilit) m(y) d(of) j(a) 486 3588 y(three-b) s(o) s(dy) i(problem,) g(whic) m(h) g(w) m(e) i(still) e (assume) h(as) h(restricted,) f(planar) g(and) 486 3696 y(circular,) 29 b(as) h(the) h(mass) f(of) h(the) f(planet) g(v) -5 b(aries.) 486 3905 y(4.1.) p Fj 65 w(Effects) 33 b(of) g(the) h (increase) f(of) h(the) f(mass) p Fv 486 4093 a(W) -8 b(e) 33 b(will) d(study) i(the) h(stabilit) m(y) f(of) g(exosolar) i (planetary) e(systems) g(with) g(a) h(large) 486 4201 y(planet) i(and) g(a) i(small) d(planet.) i(The) f(particular) g (problem) f(that) j(w) m(e) f(set) h(is) e(the) 486 4309 y(follo) m(wing:) 43 b(w) m(e) j(k) m(eep) g(the) f(semima) 5 b(jor) 45 b(axis) f(of) i(the) f(planet) f(\014xed) h(to) h(1) f(A) m (U) 486 4417 y(\(Earth-lik) m(e) 27 b(planets\)) h(and) f(v) -5 b(ary) 28 b(the) g(semima) 5 b(jor) 27 b(axis) p Fm 28 w(a) p Fl 2490 4384 a(0) p Fv 2541 4417 a(of) h(Jupiter.) f(W) -8 b(e) 29 b(will) 486 4525 y(\014nd) 34 b(the) j(range) g(of) f(v) -5 b(alues) 36 b(of) p Fm 36 w(a) p Fl 1633 4492 a(0) p Fv 1693 4525 a(\(or,) h(equiv) -5 b(alen) m(tly) d(,) 35 b(the) i(range) g(of) f(v) -5 b(alues) 36 b(of) p Fm 486 4633 a(n=n) p Fl 641 4600 a(0) p Fv 663 4633 a(\)) 31 b(for) f(whic) m(h) f(the) i(system) f(is) g(unstable.) 602 4741 y(W) -8 b(e) 30 b(fo) s(cus) f(our) 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i(di\013eren) n(t) e(v) l(alues) 486 5469 y(of) h(the) f(a) n(v) n(erage) h(eccen) n(tricit) n(y) -6 b(.) 23 b(Dashed) f(straigh) n(t) h(lines) h(at) p Fp 23 w(\006) p Fr(2) e(indicate) h(the) f(b) r(oundary) g(of) h(the) 486 5560 y(stabilit) n(y/instabilit) n(y) f(region.) h(Diamonds) d(corresp) r(ond) i(to) g(I) f(p.o.,) h(while) g(stars) g(denote) g(I) r(I) e (p.o.) p Fn 1902 5847 a(cchv-r5.tex;) 42 b(27/09/2001;) g(9:54;) e (p.12) p 90 rotate dyy eop %%Page: 13 13 13 12 bop Fv 3184 100 a(13) 486 291 y(a) 36 b(planet,) g(b) s(ecause) g (the) g(v) -5 b(ariations) 35 b(of) h(the) g(distance) g(from) g(the) g (Sun) e(will) g(b) s(e) 486 399 y(small,) 39 b(implying) f(that) j(the) g(v) -5 b(ariations) 40 b(of) h(the) h(climate) e(will) e(b) s(e) j (also) g(small) 486 506 y(during) 28 b(one) i("y) m(ear".) 602 614 y(Tw) m(o) i(di\013eren) m(t) f(cases) h(will) d(b) s(e) i(in) m(v) m(estigated:) p Fm 33 w(a) p Fl 2273 581 a(0) p Fm 2324 614 a(>) p Fv 27 w(1) h(A) m(U) g(and) p Fm 31 w(a) p Fl 2890 581 a(0) p Fm 2941 614 a(<) p Fv 27 w(1) g(A) m(U.) 486 722 y(In) j(the) h(\014rst) g(case) h(the) f(orbit) f(of) i(the) f (planet) g(\() p Fm(a) p Fv 35 w(=) f(1) h(A) m(U\)) h(is) f(an) g (inner) e(orbit) 486 830 y(and) i(in) g(the) i(second) f(case) h(it) f (is) f(an) h(outer) h(orbit.) e(W) -8 b(e) 39 b(will) 34 b(study) j(separately) 486 938 y(these) 30 b(t) m(w) m(o) i(cases,) g (although) d(they) i(are) g(similar) c(in) j(man) m(y) g(asp) s(ects.) 602 1046 y(W) -8 b(e) 38 b(remark) f(that) h(a) g(mo) s(del) e(with) g (a) h(circular) f(orbit) g(of) h(Jupiter) f(ma) m(y) i(not) 486 1154 y(b) s(e) e(realistic,) g(as) i(a) g(more) f(realistic) f(mo) s (del) g(w) m(ould) g(ha) m(v) m(e) j(an) e(elliptic) e(orbit) h(of) 486 1262 y(Jupiter.) 21 b(Ho) m(w) m(ev) m(er,) k(as) e(far) f(as) p Ff 23 w(instabilit) m(y) p Fv 20 w(is) g(concerned,) h(if) f(the) h (circular) e(mo) s(del) 486 1370 y(is) 47 b(unstable,) h(then) g(the) g (elliptic) e(mo) s(del) i(is) f(also) i(unstable.) e(Consequen) m(tly) -8 b(,) 486 1478 y(the) 48 b(results) f(obtained) h(with) f(a) i (circular) e(mo) s(del) g(are) i(also) f(v) -5 b(alid) 47 b(for) h(more) 486 1586 y(complicated) 30 b(mo) s(dels.) 486 1829 y(4.2.) p Fj 65 w(Inner) j(orbits,) p Fm 33 w(a) p Fl 1378 1796 a(0) p Fm 1427 1829 a(>) p Fv 25 w(1) p Fj 35 w(A) m(U) p Fv 486 2042 a(Let) c(us) f(start) h(with) f(the) h (unp) s(erturb) s(ed) c(problem) i(\() p Fm(m) p Fi 2330 2056 a(J) p Fv 2405 2042 a(=) e(0\),) k(with) f(Jupiter) f(de-) 486 2150 y(scribing) c(a) k(circular) d(orbit) h(with) f(radius) p Fm 25 w(a) p Fl 1954 2117 a(0) p Fv 1977 2150 a(.) i(There) f(exists) h (a) g(family) f(of) h(circular) 486 2258 y(orbits) g(of) i(the) g (small) e(planet,) i(with) e(semima) 5 b(jor) 27 b(axis) p Fm 27 w(a) e(<) g(a) p Fl 2575 2225 a(0) p Fv 2599 2258 a(,) j(along) f(whic) m(h) g(the) 486 2366 y(radius) p Fm 19 w(a) p Fv 20 w(of) 22 b(the) f(planet) f(v) -5 b(aries) 20 b(\(w) m(e) i(k) m(eep) g(the) f(v) -5 b(alue) 20 b(of) p Fm 21 w(a) p Fl 2446 2333 a(0) p Fv 2490 2366 a(\014xed\).) h(Equiv) -5 b(alen) m(tly) d(,) 486 2474 y(the) 29 b(ratio) p Fm 30 w(n=n) p Fl 1013 2441 a(0) p Fv 1065 2474 a(v) -5 b(aries) 29 b(along) h(the) f(family) -8 b(,) 29 b(appro) m(ximately) g(b) s(et) m(w) m(een) h(v) -5 b(alues) 29 b(1) 486 2582 y(\(close) i(to) g(Jupiter\)) e(and) p Fk 29 w(1) p Fv 30 w(\(v) m(ery) i(far) g(from) e(Jupiter) g(and) h (close) g(to) h(the) g(Sun\).) 486 2690 y(When) p Fm 31 w(m) p Fi 832 2704 a(J) p Fv 912 2690 a(is) f(nonzero,) i(the) f(ab) s(o) m(v) m(e) i(circular) d(orbits) g(of) i(the) f(small) f(planet) h (are) 486 2798 y(con) m(tin) m(ued) 36 b(as) g(nearly) f(circular) g(p) s(erio) s(dic) f(orbits) h(in) g(a) p Ff 36 w(syno) s(dic) g(system) p Fv(.) i(The) 486 2906 y(con) m(tin) m(uation) 30 b(is) f(not) i(p) s (ossible) d(only) h(at) i(the) g(resonances) g(2/1,) h(3/2) f(...) 602 3014 y(In) 24 b(this) g(study) h(w) m(e) g(will) e(consider) h(nearly) g (circular) g(orbits) g(of) h(the) g(planet,) g(for) 486 3122 y(a) g(range) h(of) g(v) -5 b(alues) 25 b(of) p Fm 26 w(n=n) p Fl 1418 3089 a(0) p Fv 1466 3122 a(larger) g(than) g (2/1.) j(F) -8 b(or) 26 b(smaller) e(v) -5 b(alues) 25 b(of) p Fm 25 w(n=n) p Fl 3100 3089 a(0) p Fv 3149 3122 a(the) 486 3230 y(planet) d(is) g(closer) h(to) h(Jupiter,) d(and) h (the) i(region) e(is) g(more) h(unstable.) f(In) h(the) g(ab) s(o) m(v) m(e) 486 3337 y(resonance) j(region,) f(2) p Fm(=) p Fv(1) p Fm 27 w(<) g(n=n) p Fl 1602 3304 a(0) p Fm 1650 3337 a(<) p Fk 25 w(1) p Fv(,) g(the) h(con) m(tin) m(uation) f(of) h (an) g(unp) s(erturb) s(ed) 486 3445 y(circular) 32 b(orbit) h(of) h (the) g(planet) f(to) h(the) g(case) p Fm 35 w(m) p Fi 2142 3459 a(J) p Fm 2222 3445 a(>) p Fv 30 w(0) h(is) d(p) s(ossible.) g (Therefore,) 486 3553 y(there) 27 b(exists) f(a) i(branc) m(h) e(of) h (nearly) f(circular) f(orbits) h(of) h(the) g(small) f(planet) g(in) g (the) 486 3661 y(ab) s(o) m(v) m(e) 31 b(range) g(of) p Fm 30 w(n=n) p Fl 1249 3628 a(0) p Fv 1272 3661 a(.) 602 3769 y(It) j(can) g(b) s(e) g(pro) m(v) m(en) g(that) h(instabilit) m (y) d(dev) m(elops) i(only) f(in) g(a) h(region) g(close) g(to) 486 3877 y(the) 28 b(3/1) h(resonance.) g(F) -8 b(or) 29 b(small) e(v) -5 b(alues) 28 b(of) p Fm 28 w(m) p Fi 2089 3891 a(J) p Fv 2166 3877 a(the) g(unstable) f(region) h(is) f (small,) 486 3985 y(but) e(extends) h(and) g(co) m(v) m(ers) i(a) e (large) h(part) f(of) g(the) h(phase) f(space) h(as) p Fm 26 w(m) p Fi 2825 3999 a(J) p Fv 2900 3985 a(increases.) 486 4093 y(F) -8 b(rom) 30 b(the) g(n) m(umerical) f(computations) h(w) m (e) g(found) f(also) h(that) h(as) p Fm 30 w(m) p Fi 2821 4107 a(J) p Fv 2900 4093 a(increases,) 486 4201 y(the) g(osculating) g(eccen) m(tricit) m(y) i(of) f(the) f("circular") g(p) s(erio) s(dic) e(orbits) h(is) h(not) h(v) m(ery) 486 4309 y(small.) 41 b(This) g(means) h(that) i(ev) m(en) f(if) e(the) i (orbit) f(is) g(stable,) g(the) h(v) -5 b(ariations) 42 b(of) 486 4417 y(its) 28 b(eccen) m(tricit) m(y) i(are) g(quite) e (large,) i(implying) c(large) j(v) -5 b(ariations) 28 b(of) h(the) g(climate) 486 4525 y(during) c(a) i("y) m(ear".) i(This) d (ma) m(y) i(not) f(b) s(e) g(fa) m(v) m(orable) h(for) f(the) g(dev) m (elopmen) m(t) h(of) f(life.) 602 4633 y(In) 21 b(Figure) g(4) h(w) m (e) g(presen) m(t) g(the) g(stabilit) m(y) e(index) h(of) h(v) -5 b(arious) 20 b(families) g(of) i(nearly) 486 4741 y(circular) 33 b(p) s(erio) s(dic) g(orbits) h(of) h(the) g(small) f(planet,) g(in) g (the) i(rotating) f(frame,) g(for) 486 4848 y(di\013eren) m(t) c(v) -5 b(alues) 32 b(of) p Fm 33 w(\026) p Fk 28 w(\021) p Fm 29 w(m) p Fi 1488 4862 a(J) p Fm 1537 4848 a(=) p Fv(\() p Fm(m) p Fi 1697 4862 a(S) p Fv 1770 4848 a(+) p Fm 21 w(m) p Fi 1942 4862 a(J) p Fv 1991 4848 a(\).) h(They) f(corresp) s (ond) f(to) i(the) g(range) p Fn 1902 5847 a(cchv-r5.tex;) 42 b(27/09/2001;) g(9:54;) e(p.13) p 90 rotate dyy eop %%Page: 14 14 14 13 bop Fv 486 100 a(14) 1290 1389 y @beginspecial 52 @llx 150 @lly 556 @urx 639 @ury 1417 @rwi 1417 @rhi @setspecial %%BeginDocument: figure4.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 52 150 556 639 %%Creator: CorelDRAW 8 %%Title: C:\ROMA-01\PAPER-AL\Fig4.eps %%CreationDate: Fri Aug 31 12:41:55 2001 %%DocumentProcessColors: Cyan Magenta Yellow Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness false def /AutoSteps 0 def /CMYKMarks true def /UseLevel 1 def %Color profile: PROFILES.CCM - Generic CMYK printer profile %%BeginResource: procset wCorel8Dict 8.0 0 /wCorel8Dict 300 dict def wCorel8Dict begin % Copyright (c)1992-97 Corel Corporation % All rights reserved. v8.0 r0.7 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if systemdict/CorelLexDict known{1 systemdict/CorelLexDict get exec}if}bd /@EndSysCorelDict{systemdict/Corel30Dict known{end}if/EndCorelLexDict where {pop EndCorelLexDict}if}bd AutoFlatness{/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint where{pop}{/setoverprint{ /$op xd}bd}ifelse/currentoverprint where{pop}{/currentoverprint{$op}bd}ifelse /@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd /@trp{exch pop 5 1 roll @tc_5}bd/setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll pop pop pop pop 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$k $n $o @scc_5 pop $ctm setmatrix 72 1000 div dup matrix scale dup concat dup Bburx exch Bbury exch itransform ceiling cvi/Bbury xd ceiling cvi/Bburx xd Bbllx exch Bblly exch itransform floor cvi/Bblly xd floor cvi/Bbllx xd $Prm aload pop $Psn load exec }{1 SetGry wfill}ifelse @rs @np}bd/F{matrix currentmatrix $sdf{$scf $sca $scp @ss}if $fil 1 eq{@pf}{$fil 2 eq{@ff}{$fil 3 eq{@Pf}{$t $c $m $y $k $n $o @scc_5 {wfill}{@np}ifelse}ifelse}ifelse}ifelse $sdf{$dsf $dsa $dsp @ss}if setmatrix} bd/f{@cp F}bd/S{matrix currentmatrix $ctm setmatrix $SDF{$SCF $SCA $SCP @ss}if $T $C $M $Y $K $N $O @scc_5{matrix currentmatrix $ptm concat stroke setmatrix} {@np}ifelse $SDF{$dsf $dsa $dsp @ss}if setmatrix}bd/s{@cp S}bd/B{@gs F @gr S} bd/b{@cp B}bd/_E{5 array astore exch cvlit xd}bd/@cc{currentfile $dat readhexstring pop}bd/@sm{/$ctm $ctm currentmatrix def}bd/@E{/Bbury xd/Bburx xd /Bblly xd/Bbllx xd}bd/@c{@cp}bd/@p{/$fil 1 def 1 eq dup/$vectpat xd{/$pfrg true def}{@gs $t $c $m $y $k $n $o @scc_5/$pfrg xd @gr}ifelse/$pm xd/$psy xd/$psx xd /$pyf xd/$pxf xd/$pn xd}bd/@P{/$fil 3 def/$Psn xd/$Psc xd array astore/$Prm xd }bd/@ii{concat 3 index 3 index m 3 index 1 index l 2 copy l 1 index 3 index l 3 index 3 index l clip pop pop pop pop}bd/tcc{@cc}def/@i{@sm @gs @ii 6 index 1 ne {/$frg true def pop pop}{1 eq{s1t s1c s1m s1y s1k s1n $O @scc_5/$frg xd}{/$frg false def}ifelse 1 eq{@gs $ctm setmatrix F @gr}if}ifelse @np/$ury xd/$urx xd /$lly xd/$llx xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul 8 div ceiling cvi string def $bkg $frg or{$SDF{$SCF $SCA $SCP @ss}if $llx $lly Tl $urx $llx sub $ury $lly sub scale $bkg{$t $c $m $y $k $n $o @scc_5 pop}if $wid $hei abs $bts 1 eq{$bkg}{$bts}ifelse[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/tcc load $bts 1 eq{imagemask}{image}ifelse $SDF{$dsf $dsa $dsp @ss}if}{$hei abs{tcc pop} repeat}ifelse @gr $ctm setmatrix}bd/@I{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd /$llx xd/$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $llx $lly Tl $urx $llx sub $ury $lly sub scale $wid $hei abs $bts[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/@cc load false $ncl ColorImage $SDF{$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd/COMP 0 def /MaskedImage false def L2?{/@I_2{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd/$llx xd/$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $ncl 1 eq{/DeviceGray}{$ncl 3 eq{/DeviceRGB}{/DeviceCMYK} ifelse}ifelse setcolorspace $llx $lly Tl $urx $llx sub $ury $lly sub scale 8 dict begin/ImageType 1 def/Width $wid def/Height $hei abs def/BitsPerComponent $bts def/Decode $ncl 1 eq{[0 1]}{$ncl 3 eq{[0 1 0 1 0 1]}{[0 1 0 1 0 1 0 1]} ifelse}ifelse def/ImageMatrix[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]def /DataSource currentfile/ASCII85Decode filter COMP 1 eq{/DCTDecode filter}{COMP 2 eq{/RunLengthDecode filter}if}ifelse def currentdict end image $SDF{$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd}{/@I_2{}bd}ifelse/@I_3{@sm @gs @ii @np/$ury 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/$fm 0 def 260.17512 414.03770 m 259.38312 414.97370 L 258.66312 415.83770 L 257.94312 416.70170 L 257.22312 417.49370 L 256.50312 418.28570 L 255.78312 419.07770 L 255.06312 419.79770 L 254.41512 420.51770 L 253.69512 421.23770 L 253.04712 421.88598 L 252.32712 422.53398 L 251.67912 423.10998 L 251.03112 423.68598 L 250.38312 424.26198 L 249.73512 424.76598 L 249.08712 425.19798 L 248.43912 425.70198 L 247.79112 426.06198 L 247.14312 426.49398 L 246.56712 426.85398 L 245.91912 427.14198 L 245.34312 427.42998 L 244.69512 427.64598 L 244.11912 427.86198 L 243.54312 428.07798 L 242.96712 428.22198 L 242.39112 428.29398 L 241.81512 428.36598 L 241.23912 428.36598 L 240.66312 428.36598 L 240.08712 428.36598 L 239.58312 428.29398 L 239.00683 428.14998 L 238.50283 428.00598 L 237.92683 427.86198 L 237.42283 427.64598 L 236.84683 427.35798 L 236.34283 427.06998 L 235.83883 426.78198 L 235.33483 426.42198 L 234.83083 425.98998 L 234.25483 425.55798 L 233.82283 425.12598 L 233.31883 424.54998 L 232.81483 424.04598 L 232.31083 423.46998 L 231.87883 422.82198 L 231.30283 422.17398 L 230.87083 421.52570 L 230.36683 420.73370 L 229.93483 420.01370 L 229.50283 419.22170 L 228.99883 418.35770 L 228.56683 417.49370 L 228.06283 416.62970 L 227.63083 415.69370 L 227.19883 414.68570 L 226.76683 413.67770 L 226.40683 412.66970 L 225.90283 411.58970 L 225.54283 410.50970 L 225.11083 409.35770 L 224.67883 408.13370 L 224.24683 406.98170 L 223.81483 405.68570 L 223.45483 404.46170 L 223.02283 403.16570 L 222.66283 401.79770 L 222.23083 400.42970 L 221.87083 399.06170 L 221.43883 397.62170 L 221.07883 396.18170 L S %%PageTrailer @rs @rs %%Trailer @EndSysCorelDict end %%DocumentSuppliedResources: procset wCorel8Dict %%EOF %%EndDocument @endspecial Ft 486 1590 a(Figur) l(e) 29 b(4.) p Fr 39 w(The) e(stabilit) n(y) h(index) f(of) h(inner) f(nearly) h(circular) g (p) r(erio) r(dic) h(orbits,) f(as) g(a) g(function) 486 1681 y(of) c(the) g(mean) f(v) l(alue) h(of) h(the) e(ratio) p Fq 25 w(n=n) p Fb 1630 1649 a(0) p Fr 1654 1681 a(.) h(As) p Fq 24 w(\026) p Fr 24 w(increases,) i(the) d(unstable) h(region) h (increases) g(as) 486 1772 y(w) n(ell,) i(and) e(mo) n(v) n(es) g(to) n (w) n(ards) h(smaller) g(v) l(alues) g(of) p Fq 26 w(n=n) p Fb 2038 1740 a(0) p Fr 2062 1772 a(,) g(i.e.) h(closer) f(to) g (Jupiter.) 1290 3196 y @beginspecial 41 @llx 149 @lly 570 @urx 640 @ury 1417 @rwi 1417 @rhi @setspecial %%BeginDocument: figure5.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 41 149 570 640 %%Creator: CorelDRAW 8 %%Title: C:\ROMA-01\PAPER-AL\Fig5.eps %%CreationDate: Fri Aug 31 12:39:02 2001 %%DocumentProcessColors: Cyan Magenta Yellow Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness false def /AutoSteps 0 def /CMYKMarks true def /UseLevel 1 def %Color profile: PROFILES.CCM - Generic CMYK printer profile %%BeginResource: procset wCorel8Dict 8.0 0 /wCorel8Dict 300 dict def wCorel8Dict begin % Copyright (c)1992-97 Corel Corporation % All rights reserved. v8.0 r0.7 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if systemdict/CorelLexDict known{1 systemdict/CorelLexDict get exec}if}bd /@EndSysCorelDict{systemdict/Corel30Dict known{end}if/EndCorelLexDict where {pop EndCorelLexDict}if}bd AutoFlatness{/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint where{pop}{/setoverprint{ /$op xd}bd}ifelse/currentoverprint where{pop}{/currentoverprint{$op}bd}ifelse /@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd /@trp{exch pop 5 1 roll @tc_5}bd/setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll pop pop pop pop SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry} ifelse}ifelse}bd/findcmykcustomcolor where{pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{/setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{CurrentInkName_5 eq{4 index}{0} ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd}ifelse/@scc_5{dup type /booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor}ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd/colorimage where{pop /ColorImage{colorimage}def}{/ColorImage{/ncolors xd pop/dataaq xd{dataaq ncolors dup 3 eq{/$dat xd 0 1 $dat length 3 div 1 sub{dup 3 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length 3 idiv getinterval pop}{4 eq{/$dat xd 0 1 $dat length 4 div 1 sub{dup 4 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div $dat 4 index 3 add get 255 div cmyk2rgb rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length ncolors idiv getinterval}if}ifelse}image}bd }ifelse/setcmykcolor{1 5 1 roll _ currentoverprint @scc_5/$ffpnt xd}bd /currentcmykcolor{0 0 0 0}bd/setrgbcolor{rgb2cmyk setcmykcolor}bd /currentrgbcolor{currentcmykcolor cmyk2rgb}bd/sethsbcolor{hsb2rgb setrgbcolor} bd/currenthsbcolor{currentrgbcolor rgb2hsb}bd/setgray{dup dup setrgbcolor}bd /currentgray{currentrgbcolor rgb2g}bd/InsideDCS false def/IMAGE systemdict /image get def/image{InsideDCS{IMAGE}{/EPSDict where{pop SepMode_5 0 eq{IMAGE} {dup type/dicttype eq{dup/ImageType get 1 ne{IMAGE}{dup dup/BitsPerComponent get 8 eq exch/BitsPerComponent get 1 eq or currentcolorspace 0 get/DeviceGray eq and{CurrentInkName_5(Black)eq{IMAGE}{dup/DataSource get/TCC xd/Height get abs{TCC pop}repeat}ifelse}{IMAGE}ifelse}ifelse}{2 index 1 ne{CurrentInkName_5 (Black)eq{IMAGE}{/TCC xd pop pop exch pop abs{TCC pop}repeat}ifelse}{IMAGE} ifelse}ifelse}ifelse}{IMAGE}ifelse}ifelse}bd}ifelse/WaldoColor_5 true def/@sft {$tllx $pxf add dup $tllx gt{$pwid sub}if/$tx xd $tury $pyf sub dup $tury lt {$phei add}if/$ty xd}bd/@stb{pathbbox/$ury xd/$urx xd/$lly xd/$llx xd}bd/@ep{{ cvx exec}forall}bd/@tp{@sv/$in true def 2 copy dup $lly le{/$in false def}if $phei sub $ury ge{/$in false def}if dup $urx ge{/$in false def}if $pwid add $llx le{/$in false def}if $in{@np 2 copy m $pwid 0 rl 0 $phei neg rl $pwid neg 0 rl 0 $phei rl clip @np $pn cvlit load aload pop 7 -1 roll 5 index sub 7 -1 roll 3 index sub Tl matrix currentmatrix/$ctm xd @ep pop pop pop pop}{pop pop }ifelse @rs}bd/@th{@sft 0 1 $tly 1 sub{dup $psx mul $tx add{dup $llx gt{$pwid sub}{exit}ifelse}loop exch $phei mul $ty exch sub 0 1 $tlx 1 sub{$pwid mul 3 copy 3 -1 roll add exch @tp pop}for pop pop}for}bd/@tv{@sft 0 1 $tlx 1 sub{dup $pwid mul $tx add exch $psy mul $ty exch sub{dup $ury lt{$phei add}{exit} ifelse}loop 0 1 $tly 1 sub{$phei mul 3 copy sub @tp pop}for pop pop}for}bd/$fm 0 def/wfill{1 $fm eq{fill}{eofill}ifelse}bd/wclip{1 $fm eq{clip}{eoclip}ifelse }bd/@pf{@gs $ctm setmatrix $pm concat @stb wclip @sv Bburx Bbury $pm itransform /$tury xd/$turx xd Bbllx Bblly $pm itransform/$tlly xd/$tllx xd newpath $tllx $tlly m $tllx $tury l $turx $tury l $turx $tlly l $tllx $tlly m @cp pathbbox @rs/$tury xd/$turx xd/$tlly xd/$tllx xd/$wid $turx $tllx sub def/$hei $tury $tlly sub def @gs $vectpat{1 0 0 0 0 _ $o @scc_5{wfill}if}{$t $c $m $y $k $n $o @scc_5{SepMode_5 0 eq $pfrg or{$tllx $tlly Tl $wid $hei scale <00> 8 1 false[8 0 0 1 0 0]{}imagemask}{/$bkg true def}ifelse}if}ifelse @gr $wid 0 gt $hei 0 gt and{$pn cvlit load aload pop/$pd xd 3 -1 roll sub/$phei xd exch sub/$pwid xd $wid $pwid div ceiling 1 add/$tlx xd $hei $phei div ceiling 1 add/$tly xd $psx 0 eq{@tv}{@th}ifelse}if @gr @np/$bkg false def}bd/@Pf{@sv SepMode_5 0 eq $Psc 0 ne or $ink_5 3 eq or{0 J 0 j[]0 d $t $c $m $y $k $n $o @scc_5 pop $ctm setmatrix 72 1000 div dup matrix scale dup concat dup Bburx exch Bbury exch itransform ceiling cvi/Bbury xd ceiling cvi/Bburx xd Bbllx exch Bblly exch itransform floor cvi/Bblly xd floor cvi/Bbllx xd $Prm aload pop $Psn load exec }{1 SetGry wfill}ifelse @rs @np}bd/F{matrix currentmatrix $sdf{$scf $sca $scp @ss}if $fil 1 eq{@pf}{$fil 2 eq{@ff}{$fil 3 eq{@Pf}{$t $c $m $y $k $n $o @scc_5 {wfill}{@np}ifelse}ifelse}ifelse}ifelse $sdf{$dsf $dsa $dsp @ss}if setmatrix} bd/f{@cp F}bd/S{matrix currentmatrix $ctm setmatrix $SDF{$SCF $SCA $SCP @ss}if $T $C $M $Y $K $N $O @scc_5{matrix currentmatrix $ptm concat stroke setmatrix} {@np}ifelse $SDF{$dsf $dsa $dsp @ss}if setmatrix}bd/s{@cp S}bd/B{@gs F @gr S} bd/b{@cp B}bd/_E{5 array astore exch cvlit xd}bd/@cc{currentfile $dat readhexstring pop}bd/@sm{/$ctm $ctm currentmatrix def}bd/@E{/Bbury xd/Bburx xd /Bblly xd/Bbllx xd}bd/@c{@cp}bd/@p{/$fil 1 def 1 eq dup/$vectpat xd{/$pfrg true def}{@gs $t $c $m $y $k $n $o @scc_5/$pfrg xd @gr}ifelse/$pm xd/$psy xd/$psx xd /$pyf xd/$pxf xd/$pn xd}bd/@P{/$fil 3 def/$Psn xd/$Psc xd array astore/$Prm xd }bd/@ii{concat 3 index 3 index m 3 index 1 index l 2 copy l 1 index 3 index l 3 index 3 index l clip pop pop pop pop}bd/tcc{@cc}def/@i{@sm @gs @ii 6 index 1 ne {/$frg true def pop pop}{1 eq{s1t s1c s1m s1y s1k s1n $O @scc_5/$frg xd}{/$frg false def}ifelse 1 eq{@gs $ctm setmatrix F @gr}if}ifelse @np/$ury xd/$urx xd /$lly xd/$llx xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul 8 div ceiling cvi string def $bkg $frg or{$SDF{$SCF $SCA $SCP @ss}if $llx $lly Tl $urx $llx sub $ury $lly sub scale $bkg{$t $c $m $y $k $n $o @scc_5 pop}if $wid $hei abs $bts 1 eq{$bkg}{$bts}ifelse[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/tcc load $bts 1 eq{imagemask}{image}ifelse $SDF{$dsf $dsa $dsp @ss}if}{$hei abs{tcc pop} repeat}ifelse @gr $ctm setmatrix}bd/@I{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd /$llx xd/$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $llx $lly Tl $urx $llx sub $ury $lly sub scale $wid $hei abs $bts[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/@cc load false $ncl ColorImage $SDF{$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd/COMP 0 def /MaskedImage false def L2?{/@I_2{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd/$llx xd/$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $ncl 1 eq{/DeviceGray}{$ncl 3 eq{/DeviceRGB}{/DeviceCMYK} ifelse}ifelse setcolorspace $llx $lly Tl $urx $llx sub $ury $lly sub scale 8 dict begin/ImageType 1 def/Width $wid def/Height $hei abs def/BitsPerComponent $bts def/Decode $ncl 1 eq{[0 1]}{$ncl 3 eq{[0 1 0 1 0 1]}{[0 1 0 1 0 1 0 1]} ifelse}ifelse def/ImageMatrix[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]def /DataSource currentfile/ASCII85Decode filter COMP 1 eq{/DCTDecode filter}{COMP 2 eq{/RunLengthDecode filter}if}ifelse def currentdict end image $SDF{$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd}{/@I_2{}bd}ifelse/@I_3{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd/$llx xd/$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $ncl 1 eq{/DeviceGray}{$ncl 3 eq {/DeviceRGB}{/DeviceCMYK}ifelse}ifelse setcolorspace $llx $lly Tl $urx $llx sub $ury $lly sub scale/ImageDataDict 8 dict def ImageDataDict begin/ImageType 1 def/Width $wid def/Height $hei abs def/BitsPerComponent $bts def/Decode $ncl 1 eq{[0 1]}{$ncl 3 eq{[0 1 0 1 0 1]}{[0 1 0 1 0 1 0 1]}ifelse}ifelse def /ImageMatrix[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]def/DataSource currentfile/ASCII85Decode filter COMP 1 eq{/DCTDecode filter}{COMP 2 eq{ /RunLengthDecode filter}if}ifelse def end/MaskedImageDict 7 dict def MaskedImageDict begin/ImageType 3 def/InterleaveType 3 def/MaskDict ImageMaskDict def/DataDict ImageDataDict def end MaskedImageDict image $SDF {$dsf $dsa $dsp @ss}if @gr $ctm setmatrix}bd/@SetMask{/$mbts xd/$mhei xd/$mwid xd/ImageMaskDict 8 dict def ImageMaskDict begin/ImageType 1 def/Width $mwid def /Height $mhei abs def/BitsPerComponent $mbts def/DataSource maskstream def /ImageMatrix[$mwid 0 0 $mhei neg 0 $mhei 0 gt{$mhei}{0}ifelse]def/Decode[1 0] def end}bd/@B{@gs S @gr F}bd/@b{@cp @B}bd/@sep{CurrentInkName_5(Composite)eq {/$ink_5 -1 def}{CurrentInkName_5(Cyan)eq{/$ink_5 0 def}{CurrentInkName_5 (Magenta)eq{/$ink_5 1 def}{CurrentInkName_5(Yellow)eq{/$ink_5 2 def}{ CurrentInkName_5(Black)eq{/$ink_5 3 def}{/$ink_5 4 def}ifelse}ifelse}ifelse} ifelse}ifelse}bd/@whi{@gs -72000 dup m -72000 72000 l 72000 dup l 72000 -72000 l @cp 1 SetGry fill @gr}bd/@neg{[{1 exch sub}/exec cvx currenttransfer/exec cvx]cvx settransfer @whi}bd/deflevel 0 def/@sax{/deflevel deflevel 1 add def} bd/@eax{/deflevel deflevel dup 0 gt{1 sub}if def deflevel 0 gt{/eax load}{eax} ifelse}bd/eax{{exec}forall}bd/@rax{deflevel 0 eq{@rs @sv}if}bd/@daq{dup type /arraytype eq{{}forall}if}bd/@BMP{/@cc xd UseLevel 3 eq MaskedImage true eq and {7 -2 roll pop pop @I_3}{12 index 1 gt UseLevel 2 eq UseLevel 3 eq or and{7 -2 roll pop pop @I_2}{11 index 1 eq{12 -1 roll pop @i}{7 -2 roll pop pop @I} ifelse}ifelse}ifelse}bd systemdict/pdfmark known not{/pdfmark/cleartomark ld} if /z{exch findfont exch scalefont setfont}bd/ZB{9 dict dup begin 4 1 roll /FontType 3 def/FontMatrix xd/FontBBox xd/Encoding 256 array def 0 1 255{ Encoding exch/.notdef put}for/CharStrings 256 dict def CharStrings/.notdef{} put/Metrics 256 dict def Metrics/.notdef 3 -1 roll put/BuildChar{exch dup /$char exch/Encoding get 3 index get def dup/Metrics get $char get aload pop setcachedevice begin Encoding exch get CharStrings exch get end exec}def end definefont pop}bd/ZBAddChar{findfont begin dup 4 1 roll dup 6 1 roll Encoding 3 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@endspecial Ft 486 3398 a(Figur) l(e) g(5.) p Fr 38 w(The) f(unstable) f (region) h(as) g(a) f(function) g(of) p Fq 25 w(\026) p Fr(,) h(for) g(inner) f(orbits.) h(The) f(v) l(alues) g(of) h(the) 486 3488 y(mean) f(eccen) n(tricit) n(y) i(are) g(also) h(indicated) f(at) g (the) f(b) r(oundaries.) p Fv 486 3877 a(of) p Fm 27 w(n=n) p Fl 741 3844 a(0) p Fv 790 3877 a(from) h(2) i(to) f(3.4) h(.) f (The) f(range) h(of) g(the) g(v) -5 b(alues) 27 b(of) p Fm 27 w(\026) p Fv 26 w(is) f(b) s(et) m(w) m(een) h(0.01) i(and) 486 3985 y(0.25.) j(W) -8 b(e) 31 b(ha) m(v) m(e) h(instabilit) m(y) c(if) h (the) i(stabilit) m(y) e(index) g(is) g(smaller) g(than) p Fk 30 w(\000) p Fv(2.) 602 4093 y(>F) -8 b(rom) 36 b(Figure) f(4) g(w) m (e) h(can) g(also) f(deduce) g(that) h(the) p Ff 36 w(Kirkw) m(o) s(o) s (d) d(gaps) p Fv 36 w(in) h(an) 486 4201 y(exosolar) 24 b(planetary) f(system) i(with) d(a) j(large) f("Jupiter") f(should) f (b) s(e) h(m) m(uc) m(h) h(larger) 486 4309 y(than) 30 b(that) h(in) e(the) h(asteroid) g(b) s(elt) g(of) g(our) g(Solar) g (System.) 602 4417 y(In) h(Figure) g(5) h(w) m(e) g(plot) f(the) g (minim) m(um) e(and) i(the) h(maxim) m(um) e(v) -5 b(alue) 31 b(of) p Fm 32 w(n=n) p Fl 3227 4384 a(0) p Fv 3250 4417 a(,) 486 4525 y(for) c(eac) m(h) h(v) -5 b(alue) p Fm 27 w(\026) p Fv(,) 28 b(as) f(obtained) g(from) g(Figure) g(4.) h(W) -8 b(e) 29 b(also) e(indicate) f(the) i(mean) 486 4633 y(v) -5 b(alues) 23 b(of) i(the) g(osculating) e(eccen) m(tricities,) i(at) g (the) g(b) s(oundaries) d(of) j(the) f(unstable) 486 4741 y(region,) h(for) g(di\013eren) m(t) g(v) -5 b(alues) 24 b(of) p Fm 26 w(\026) p Fv(.) h(Note) i(that) f(the) f(eccen) m(tricit) m(y) i(is) d(quite) h(large) 486 4848 y(for) 30 b(large) g(v) -5 b(alues) 30 b(of) p Fm 30 w(\026) p Fv(.) p Fn 1902 5847 a(cchv-r5.tex;) 42 b(27/09/2001;) g(9:54;) e(p.14) p 90 rotate dyy eop %%Page: 15 15 15 14 bop Fv 3184 100 a(15) 1290 1389 y @beginspecial 40 @llx 147 @lly 570 @urx 642 @ury 1417 @rwi 1417 @rhi @setspecial %%BeginDocument: figure6.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 40 147 570 642 %%Creator: CorelDRAW 8 %%Title: C:\ROMA-01\PAPER-AL\Fig6.eps %%CreationDate: Fri Aug 31 12:43:32 2001 %%DocumentProcessColors: Cyan Magenta Yellow Black %%DocumentSuppliedResources: (atend) %%EndComments %%BeginProlog /AutoFlatness false def /AutoSteps 0 def /CMYKMarks true def /UseLevel 1 def %Color profile: PROFILES.CCM - Generic CMYK printer profile %%BeginResource: procset wCorel8Dict 8.0 0 /wCorel8Dict 300 dict def wCorel8Dict begin % Copyright (c)1992-97 Corel Corporation % All rights reserved. v8.0 r0.7 /bd{bind def}bind def/ld{load def}bd/xd{exch def}bd/_ null def/rp{{pop}repeat} bd/@cp/closepath ld/@gs/gsave ld/@gr/grestore ld/@np/newpath ld/Tl/translate ld /$sv 0 def/@sv{/$sv save def}bd/@rs{$sv restore}bd/spg/showpage ld/showpage{} bd currentscreen/@dsp xd/$dsp/@dsp def/$dsa xd/$dsf xd/$sdf false def/$SDF false def/$Scra 0 def/SetScr/setscreen ld/setscreen{pop pop pop}bd/@ss{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if exch $Scra add exch load SetScr}bd /SepMode_5 where{pop}{/SepMode_5 0 def}ifelse/CurrentInkName_5 where{pop} {/CurrentInkName_5(Composite)def}ifelse/$ink_5 where{pop}{/$ink_5 -1 def} ifelse/$c 0 def/$m 0 def/$y 0 def/$k 0 def/$t 1 def/$n _ def/$o 0 def/$fil 0 def/$C 0 def/$M 0 def/$Y 0 def/$K 0 def/$T 1 def/$N _ def/$O 0 def/$PF false def/s1c 0 def/s1m 0 def/s1y 0 def/s1k 0 def/s1t 0 def/s1n _ def/$bkg false def /SK 0 def/SM 0 def/SY 0 def/SC 0 def/$op false def matrix currentmatrix/$ctm xd /$ptm matrix def/$ttm matrix def/$stm matrix def/$ffpnt true def /CorelDrawReencodeVect[16#0/grave 16#5/breve 16#6/dotaccent 16#8/ring 16#A/hungarumlaut 16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave 16#7C/bar 16#82/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl 16#88/circumflex/perthousand/Scaron/guilsinglleft/OE 16#91/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash 16#98/tilde/trademark/scaron/guilsinglright/oe 16#9F/Ydieresis 16#A1/exclamdown/cent/sterling/currency/yen/brokenbar/section 16#a8/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/minus/registered/macron 16#b0/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered 16#b8/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown 16#c0/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla 16#c8/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis 16#d0/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply 16#d8/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls 16#e0/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla 16#e8/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis 16#f0/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide 16#f8/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def /L2?/languagelevel where{pop languagelevel 2 ge}{false}ifelse def /@BeginSysCorelDict{systemdict/Corel30Dict known{systemdict/Corel30Dict get exec}if systemdict/CorelLexDict known{1 systemdict/CorelLexDict get exec}if}bd /@EndSysCorelDict{systemdict/Corel30Dict known{end}if/EndCorelLexDict where {pop EndCorelLexDict}if}bd AutoFlatness{/@ifl{dup currentflat exch sub 10 gt{ ([Error: PathTooComplex; OffendingCommand: AnyPaintingOperator]\n)print flush @np exit}{currentflat 2 add setflat}ifelse}bd/@fill/fill ld/fill{currentflat{ {@fill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@eofill/eofill ld/eofill {currentflat{{@eofill}stopped{@ifl}{exit}ifelse}bind loop setflat}bd/@clip /clip ld/clip{currentflat{{@clip}stopped{@ifl}{exit}ifelse}bind loop setflat} bd/@eoclip/eoclip ld/eoclip{currentflat{{@eoclip}stopped{@ifl}{exit}ifelse} bind loop setflat}bd/@stroke/stroke ld/stroke{currentflat{{@stroke}stopped {@ifl}{exit}ifelse}bind loop setflat}bd}if L2?{/@ssa{true setstrokeadjust}bd}{ /@ssa{}bd}ifelse/d/setdash ld/j/setlinejoin ld/J/setlinecap ld/M/setmiterlimit ld/w/setlinewidth ld/O{/$o xd}bd/R{/$O xd}bd/W/eoclip ld/c/curveto ld/C/c ld/l /lineto ld/L/l ld/rl/rlineto ld/m/moveto ld/n/newpath ld/N/newpath ld/P{11 rp} bd/u{}bd/U{}bd/A{pop}bd/q/@gs ld/Q/@gr ld/&{}bd/@j{@sv @np}bd/@J{@rs}bd/g{1 exch sub/$k xd/$c 0 def/$m 0 def/$y 0 def/$t 1 def/$n _ def/$fil 0 def}bd/G{1 sub neg/$K xd _ 1 0 0 0/$C xd/$M xd/$Y xd/$T xd/$N xd}bd/k{1 index type /stringtype eq{/$t xd/$n xd}{/$t 0 def/$n _ def}ifelse/$k xd/$y xd/$m xd/$c xd /$fil 0 def}bd/K{1 index type/stringtype eq{/$T xd/$N xd}{/$T 0 def/$N _ def} ifelse/$K xd/$Y xd/$M xd/$C xd}bd/x/k ld/X/K ld/sf{1 index type/stringtype eq{ /s1t xd/s1n xd}{/s1t 0 def/s1n _ def}ifelse/s1k xd/s1y xd/s1m xd/s1c xd}bd/i{ dup 0 ne{setflat}{pop}ifelse}bd/v{4 -2 roll 2 copy 6 -2 roll c}bd/V/v ld/y{2 copy c}bd/Y/y ld/@w{matrix rotate/$ptm xd matrix scale $ptm dup concatmatrix /$ptm xd 1 eq{$ptm exch dup concatmatrix/$ptm xd}if 1 w}bd/@g{1 eq dup/$sdf xd {/$scp xd/$sca xd/$scf xd}if}bd/@G{1 eq dup/$SDF xd{/$SCP xd/$SCA xd/$SCF xd} if}bd/@D{2 index 0 eq{$dsf 3 1 roll 4 -1 roll pop}if 3 copy exch $Scra add exch load SetScr/$dsp xd/$dsa xd/$dsf xd}bd/$ngx{$SDF{$SCF SepMode_5 0 eq{$SCA} {$dsa}ifelse $SCP @ss}if}bd/p{/$pm xd 7 rp/$pyf xd/$pxf xd/$pn xd/$fil 1 def} bd/@MN{2 copy le{pop}{exch pop}ifelse}bd/@MX{2 copy ge{pop}{exch pop}ifelse}bd /InRange{3 -1 roll @MN @MX}bd/@sqr{dup 0 rl dup 0 exch rl neg 0 rl @cp}bd /currentscale{1 0 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt 0 1 dtransform matrix defaultmatrix idtransform dup mul exch dup mul add sqrt}bd/@unscale{}bd/wDstChck{2 1 roll dup 3 -1 roll eq{1 add}if}bd /@dot{dup mul exch dup mul add 1 exch sub}bd/@lin{exch pop abs 1 exch sub}bd /cmyk2rgb{3{dup 5 -1 roll add 1 exch sub dup 0 lt{pop 0}if exch}repeat pop}bd /rgb2cmyk{3{1 exch sub 3 1 roll}repeat 3 copy @MN @MN 3{dup 5 -1 roll sub neg exch}repeat}bd/rgb2g{2 index .299 mul 2 index .587 mul add 1 index .114 mul add 4 1 roll pop pop pop}bd/WaldoColor_5 where{pop}{/SetRgb/setrgbcolor ld/GetRgb /currentrgbcolor ld/SetGry/setgray ld/GetGry/currentgray ld/SetRgb2 systemdict /setrgbcolor get def/GetRgb2 systemdict/currentrgbcolor get def/SetHsb systemdict/sethsbcolor get def/GetHsb systemdict/currenthsbcolor get def /rgb2hsb{SetRgb2 GetHsb}bd/hsb2rgb{3 -1 roll dup floor sub 3 1 roll SetHsb GetRgb2}bd/setcmykcolor where{pop/SetCmyk_5/setcmykcolor ld}{/SetCmyk_5{ cmyk2rgb SetRgb}bd}ifelse/currentcmykcolor where{pop/GetCmyk/currentcmykcolor ld}{/GetCmyk{GetRgb rgb2cmyk}bd}ifelse/setoverprint where{pop}{/setoverprint{ /$op xd}bd}ifelse/currentoverprint where{pop}{/currentoverprint{$op}bd}ifelse /@tc_5{5 -1 roll dup 1 ge{pop}{4{dup 6 -1 roll mul exch}repeat pop}ifelse}bd /@trp{exch pop 5 1 roll @tc_5}bd/setprocesscolor_5{SepMode_5 0 eq{SetCmyk_5}{0 4 $ink_5 sub index exch pop 5 1 roll pop pop pop pop SepsColor true eq{$ink_5 3 gt{1 sub neg SetGry}{0 0 0 4 $ink_5 roll SetCmyk_5}ifelse}{1 sub neg SetGry} ifelse}ifelse}bd/findcmykcustomcolor where{pop}{/findcmykcustomcolor{5 array astore}bd}ifelse/setcustomcolor where{pop}{/setcustomcolor{exch aload pop SepMode_5 0 eq{pop @tc_5 setprocesscolor_5}{CurrentInkName_5 eq{4 index}{0} ifelse 6 1 roll 5 rp 1 sub neg SetGry}ifelse}bd}ifelse/@scc_5{dup type /booleantype eq{setoverprint}{1 eq setoverprint}ifelse dup _ eq{pop setprocesscolor_5 pop}{findcmykcustomcolor exch setcustomcolor}ifelse SepMode_5 0 eq{true}{GetGry 1 eq currentoverprint and not}ifelse}bd/colorimage where{pop /ColorImage{colorimage}def}{/ColorImage{/ncolors xd pop/dataaq xd{dataaq ncolors dup 3 eq{/$dat xd 0 1 $dat length 3 div 1 sub{dup 3 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div rgb2g 255 mul cvi exch pop $dat 3 1 roll put}for $dat 0 $dat length 3 idiv getinterval pop}{4 eq{/$dat xd 0 1 $dat length 4 div 1 sub{dup 4 mul $dat 1 index get 255 div $dat 2 index 1 add get 255 div $dat 3 index 2 add get 255 div $dat 4 index 3 add 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ifelse}ifelse}ifelse}{IMAGE}ifelse}ifelse}bd}ifelse/WaldoColor_5 true def/@sft {$tllx $pxf add dup $tllx gt{$pwid sub}if/$tx xd $tury $pyf sub dup $tury lt {$phei add}if/$ty xd}bd/@stb{pathbbox/$ury xd/$urx xd/$lly xd/$llx xd}bd/@ep{{ cvx exec}forall}bd/@tp{@sv/$in true def 2 copy dup $lly le{/$in false def}if $phei sub $ury ge{/$in false def}if dup $urx ge{/$in false def}if $pwid add $llx le{/$in false def}if $in{@np 2 copy m $pwid 0 rl 0 $phei neg rl $pwid neg 0 rl 0 $phei rl clip @np $pn cvlit load aload pop 7 -1 roll 5 index sub 7 -1 roll 3 index sub Tl matrix currentmatrix/$ctm xd @ep pop pop pop pop}{pop pop }ifelse @rs}bd/@th{@sft 0 1 $tly 1 sub{dup $psx mul $tx add{dup $llx gt{$pwid sub}{exit}ifelse}loop exch $phei mul $ty exch sub 0 1 $tlx 1 sub{$pwid mul 3 copy 3 -1 roll add exch @tp pop}for pop pop}for}bd/@tv{@sft 0 1 $tlx 1 sub{dup $pwid mul $tx add exch $psy mul $ty exch sub{dup $ury lt{$phei add}{exit} ifelse}loop 0 1 $tly 1 sub{$phei mul 3 copy sub @tp pop}for pop pop}for}bd/$fm 0 def/wfill{1 $fm eq{fill}{eofill}ifelse}bd/wclip{1 $fm eq{clip}{eoclip}ifelse }bd/@pf{@gs $ctm setmatrix $pm concat @stb wclip @sv Bburx Bbury $pm itransform /$tury xd/$turx xd Bbllx Bblly $pm itransform/$tlly xd/$tllx xd newpath $tllx $tlly m $tllx $tury l $turx $tury l $turx $tlly l $tllx $tlly m @cp pathbbox @rs/$tury xd/$turx xd/$tlly xd/$tllx xd/$wid $turx $tllx sub def/$hei $tury $tlly sub def @gs $vectpat{1 0 0 0 0 _ $o @scc_5{wfill}if}{$t $c $m $y $k $n $o @scc_5{SepMode_5 0 eq $pfrg or{$tllx $tlly Tl $wid $hei scale <00> 8 1 false[8 0 0 1 0 0]{}imagemask}{/$bkg true def}ifelse}if}ifelse @gr $wid 0 gt $hei 0 gt and{$pn cvlit load aload pop/$pd xd 3 -1 roll sub/$phei xd exch sub/$pwid xd $wid $pwid div ceiling 1 add/$tlx xd $hei $phei div ceiling 1 add/$tly xd $psx 0 eq{@tv}{@th}ifelse}if @gr @np/$bkg false def}bd/@Pf{@sv SepMode_5 0 eq $Psc 0 ne or $ink_5 3 eq or{0 J 0 j[]0 d $t $c $m $y $k $n $o @scc_5 pop $ctm setmatrix 72 1000 div dup matrix scale dup concat 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def/$Psn xd/$Psc xd array astore/$Prm xd }bd/@ii{concat 3 index 3 index m 3 index 1 index l 2 copy l 1 index 3 index l 3 index 3 index l clip pop pop pop pop}bd/tcc{@cc}def/@i{@sm @gs @ii 6 index 1 ne {/$frg true def pop pop}{1 eq{s1t s1c s1m s1y s1k s1n $O @scc_5/$frg xd}{/$frg false def}ifelse 1 eq{@gs $ctm setmatrix F @gr}if}ifelse @np/$ury xd/$urx xd /$lly xd/$llx xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul 8 div ceiling cvi string def $bkg $frg or{$SDF{$SCF $SCA $SCP @ss}if $llx $lly Tl $urx $llx sub $ury $lly sub scale $bkg{$t $c $m $y $k $n $o @scc_5 pop}if $wid $hei abs $bts 1 eq{$bkg}{$bts}ifelse[$wid 0 0 $hei neg 0 $hei 0 gt{$hei}{0}ifelse]/tcc load $bts 1 eq{imagemask}{image}ifelse $SDF{$dsf $dsa $dsp @ss}if}{$hei abs{tcc pop} repeat}ifelse @gr $ctm setmatrix}bd/@I{@sm @gs @ii @np/$ury xd/$urx xd/$lly xd /$llx xd/$ncl xd/$bts xd/$hei xd/$wid xd/$dat $wid $bts mul $ncl mul 8 div ceiling cvi string def $ngx $llx $lly Tl $urx $llx sub $ury $lly sub scale $wid $hei abs 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i(corresp) s(onding) e(resonance) j(of) g(a) f(p) s(ossible) 667 1476 y(Earth-lik) m(e) 36 b(planet) f(w) m(ould) g(b) s(e) h(equal) g (to) p Fm 37 w(n=n) p Fl 2301 1443 a(0) p Fv 2358 1476 a(=) f(57,) i(and) f(the) g(v) -5 b(alue) 36 b(of) p Fm 667 1584 a(\026) p Fv 33 w(is) d(larger) g(than) f(0.0003) k (\(assuming) c(the) i(mass) f(of) g(the) h("Sun") e(is) g(equal) 667 1692 y(to) k(0.92) g(Solar) f(mass\).) g(F) -8 b(rom) 35 b(Figure) g(6) g(w) m(e) g(see) h(that) f(it) g(is) f(w) m(ell) g (outside) 667 1800 y(the) 45 b(unstable) e(region.) h(So,) g(as) g(far) g(as) h(the) f(stabilit) m(y) f(of) h(the) g(planet) g(is) 667 1907 y(concerned,) 31 b(an) f(outer) h(Earth-lik) m(e) f(planet) g (could) f(exist.) p Fk 523 2096 a(\000) p Fv 73 w(GI86\(HD13455\)) 667 2204 y(W) -8 b(e) 33 b(ha) m(v) m(e) p Fm 33 w(M) p Fv 25 w(sin) p Fm 14 w(i) p Fv 28 w(=) 27 b(4) p Fm(M) p Fi 1566 2218 a(J) p Fv 1615 2204 a(,) p Fm 32 w(P) p Fv 13 w(=15.78) 33 b(d,) p Fm 32 w(a) p Fv(=0.11) f(A) m(U,) p Fm 33 w(e) p Fv(=0.04) h(\(Han) f(et) 667 2312 y(al.) j(\(2000\)\).) j (The) c(corresp) s(onding) f(resonance) i(of) g(a) g(p) s(ossible) e (Earth-lik) m(e) 667 2420 y(planet) i(w) m(ould) e(b) s(e) h(equal) h (to) p Fm 35 w(n=n) p Fl 1862 2387 a(0) p Fv 1918 2420 a(=) d(23,) k(and) f(the) g(v) -5 b(alue) 34 b(of) p Fm 35 w(\026) p Fv 34 w(is) g(larger) 667 2528 y(than) 29 b(0.005) h(\(assuming) e(the) h(mass) f(of) h(the) g("Sun") f(is) f (equal) h(to) i(0.79) g(Solar) 667 2636 y(mass\).) 37 b(F) -8 b(rom) 37 b(Figure) f(6) h(w) m(e) g(see) g(that) h(it) e(is) f (w) m(ell) h(outside) g(the) g(unstable) 667 2744 y(region.) k(So,) f (as) h(far) g(as) f(the) h(stabilit) m(y) e(of) i(the) g(planet) f(is) f (concerned,) i(an) 667 2852 y(outer) 31 b(Earth-lik) m(e) f(planet) g (could) f(exist.) p Fk 523 3041 a(\000) p Fv 73 w(47UMab) 667 3149 y(W) -8 b(e) 25 b(ha) m(v) m(e) p Fm 24 w(M) p Fv 26 w(sin) p Fm 13 w(i) p Fv 26 w(=) g(2) p Fm(:) p Fv(54) p Fm(M) p Fi 1660 3163 a(J) p Fv 1711 3149 a(,) p Fm 23 w(P) p Fv 13 w(=1089.0) g(d,) p Fm 23 w(a) p Fv(=2.09) g(A) m(U,) p Fm 24 w(e) p Fv(=0.06) g(\(But-) 667 3257 y(ler) k(and) h(Marcy) g (\(1996\)\).) j(The) d(corresp) s(onding) e(resonance) i(of) g(a) g(p) s (ossible) 667 3364 y(inner) 37 b(Earth-lik) m(e) h(planet) g(w) m(ould) f(b) s(e) h(equal) g(to) p Fm 39 w(n=n) p Fl 2555 3331 a(0) p Fv 2616 3364 a(=) h(2) p Fm(:) p Fv(98,) h(i.e.) f(v) m(ery) 667 3472 y(close) 22 b(to) h(the) f(unstable) f(resonance) h(3/1) h(and) e (the) h(v) -5 b(alue) 21 b(of) p Fm 22 w(\026) p Fv 22 w(is) g(larger) g(than) 667 3580 y(0.003) 35 b(\(assuming) c(the) h (mass) h(of) f(the) h("Sun") e(is) g(equal) h(to) h(1) g(Solar) f (mass\).) 667 3688 y(F) -8 b(rom) 38 b(Figure) e(5) h(w) m(e) h(see) f (that) g(an) g(Earth-lik) m(e) f(planet) h(w) m(ould) e(b) s(e) h(in) g (the) 667 3796 y(3/1) 23 b(unstable) d(zone,) j(whic) m(h) d(in) g (fact) j(is) d(the) i(corresp) s(onding) d(3/1) k(Kirkw) m(o) s(o) s(d) 667 3904 y(gap.) 30 b(Since) e(the) h(mass) f(of) h("Jupiter") f(is) g (larger) h(than) f(that) i(of) f(the) g(Jupiter) 667 4012 y(of) g(our) e(Solar) h(System,) g(the) g(instabilit) m(y) e(is) h (stronger.) h(Consequen) m(tly) -8 b(,) 28 b(it) g(is) 667 4120 y(not) 33 b(lik) m(ely) e(that) i(an) f(Earth-lik) m(e) g(planet) g (could) g(surviv) m(e) f(in) g(this) h(exosolar) 667 4228 y(system.) p Fk 523 4417 a(\000) p Fv 73 w(HD10697) 667 4525 y(W) -8 b(e) 32 b(ha) m(v) m(e) p Fm 32 w(M) p Fv 26 w(sin) p Fm 13 w(i) p Fv 27 w(=) 25 b(6) p Fm(:) p Fv(59) p Fm(M) p Fi 1676 4539 a(J) p Fv 1727 4525 a(,) p Fm 31 w(P) p Fv 13 w(=1093.0) 33 b(d,) p Fm 31 w(a) p Fv(=2.0) e(A) m(U,) p Fm 32 w(e) p Fv(=0.12) i(\(Han) 667 4633 y(et) f(al.) e(\(2000\),) j(Zuc) m(k) m(er) e(and) f(Mazeh) i (\(2000\)\).) i(The) c(corresp) s(onding) e(reso-) 667 4741 y(nance) 21 b(of) f(a) h(p) s(ossible) d(Earth-lik) m(e) i(planet) f(w) m(ould) h(b) s(e) f(equal) h(to) p Fm 21 w(n=n) p Fl 2944 4708 a(0) p Fv 2992 4741 a(=) 25 b(2) p Fm(:) p Fv(99,) 667 4848 y(i.e.) 32 b(v) m(ery) g(close) f(to) h(the) g (unstable) e(resonance) i(3/1) g(and) f(the) h(v) -5 b(alue) 30 b(of) p Fm 32 w(\026) p Fv 31 w(is) p Fn 1902 5847 a(cchv-r5.tex;) 42 b(27/09/2001;) g(9:54;) e(p.16) p 90 rotate dyy eop %%Page: 17 17 17 16 bop Fv 3184 100 a(17) 667 291 y(larger) 30 b(than) g(0.006) j (\(assuming) c(the) h(mass) g(of) h(the) f("Sun") g(is) f(equal) h(to) h (1.1) 667 399 y(Solar) 25 b(mass\).) h(F) -8 b(rom) 26 b(Figure) f(5) h(w) m(e) g(see) h(that) f(an) f(Earth-lik) m(e) g (planet) g(w) m(ould) 667 506 y(b) s(e) g(in) g(the) h(3/1) h(unstable) d(zone,) j(whic) m(h) d(in) h(fact) h(is) f(the) h(corresp) s(onding) e (3/1) 667 614 y(Kirkw) m(o) s(o) s(d) i(gap.) j(Since) d(the) i(mass) g (of) g(the) g(Jupiter) e(of) i("Jupiter") f(is) f(larger) 667 722 y(than) 33 b(that) g(of) g(our) f(Solar) f(System,) i(the) g (instabilit) m(y) d(is) h(stronger.) i(On) f(the) 667 830 y(other) f(hand,) f(the) g(eccen) m(tricit) m(y) i(of) e("Jupiter") g(is) g(not) g(v) m(ery) h(close) g(to) g(zero,) 667 938 y(but) i(this) g(is) g(exp) s(ected) h(to) h(mak) m(e) g(stronger) f (the) g(instabilit) m(y) d(obtained) i(b) m(y) 667 1046 y(the) e(circular) e(restricted) h(three-b) s(o) s(dy) g(problem) f (appro) m(ximation.) h(Conse-) 667 1154 y(quen) m(tly) -8 b(,) 33 b(it) f(is) g(not) h(lik) m(ely) e(that) i(an) f(Earth-lik) m (e) g(planet) g(could) g(surviv) m(e) f(in) 667 1262 y(this) f(exosolar) g(system.) p Fo 1446 1699 a(Ac) m(kno) m(wledgemen) m(ts) p Fv 486 1919 a(The) 44 b(results) g(on) g(the) h(in) m(terior) f (resonances) h(\(section) h(3.1\)) g(are) f(part) g(of) g(the) 486 2027 y(master) 30 b(thesis) g(b) m(y) g(A.) h(Chessa.) p Fo 1635 2464 a(References) p Fr 486 2667 a(Arnol'd) d(V.I.:) p Fa 29 w(Pro) r(of) i(of) g(a) f(Theorem) g(b) n(y) e(A.N.) i(Kolmogoro) n(v) g(on) g(the) f(in) n(v) l(ariance) h(of) g(quasi-) 602 2758 y(p) r(erio) r(dic) 37 b(motions) f(under) g(small) h(p) r (erturbations) f(of) h(the) f(Hamiltonian) p Fr(,) h(Russ.) f(Math.) 602 2848 y(Surv) n(eys) p Fs(18) p Fr(,) 25 b(9) h(\(1963\)) 486 2939 y(Butler) f(R.P) -6 b(.,) 26 b(Marcy) f(G.W.:) p Fa 27 w(A) f(planet) h(orbiting) h(47Uma) p Fr(,) f(Astroph) n(ys.) g (J.) p Fs 26 w(464) p Fr(,) h(L153-L156) 602 3030 y(\(1996\)) 486 3121 y(Hadjidemetriou) i(J.D.:) p Fa 30 w(Algebraic) i(mappings) f (near) g(a) g(resonance) h(with) g(an) f(application) h(to) 602 3212 y(asteroid) 38 b(motion) p Fr(,) f(in:) h(Long-term) e(dynamical) h (b) r(eha) n(viour) g(of) h(natural) g(and) f(arti\014cial) 602 3303 y(N-b) r(o) r(dy) 24 b(systems,) h(A.E.) i(Ro) n(y) d(ed.,) j (257-276) g(\(1988\)) 486 3394 y(Hadjidemetriou) k(J.D.:) p Fa 32 w(The) g(elliptic) i(restricted) f(problem) e(at) i(the) f(3:1) h (resonance) p Fr(,) g(Celest.) 602 3485 y(Mec) n(h.) 26 b(&) f(Dynam.) f(Astron.) p Fs 26 w(53) p Fr(,) j(151-183) g(\(1992\)) 486 3576 y(Hadjidemetriou) 20 b(J.D.:) p Fa 22 w(Symplectic) g (mappings) p Fr(,) g(Dynamics,) h(Ephemerids) f(and) g(Astrometry) 602 3667 y(of) 26 b(the) g(Solar) g(System,) e(IA) n(U,) h(255-266) j (\(1996\)) 486 3758 y(Hadjidemetriou) g(J.D.,) h(Ic) n(h) n(tiaroglou) g (S.:) p Fa 29 w(A) f(qualitativ) n(e) h(study) e(of) i(the) f(Kirkw) n (o) r(o) r(d) h(gaps) g(in) 602 3848 y(the) c(asteroids) p Fr(,) i(Astron.) f(Astroph) n(ys.) p Fs 25 w(131) p Fr(,) h(20-31) g (\(1984\)) 486 3939 y(Han) 44 b(I.,) i(Blac) n(k) g(D.,) g(Gatew) n(o) r (o) r(d) h(G.:) p Fa 46 w(Preliminary) e(astrometric) h(masses) g(for) g (prop) r(osed) 602 4030 y(extrasolar) 27 b(panetary) e(companions) p Fr(,) h(Astroph) n(ys.) f(J.) p Fs 27 w(548) p Fr(,) h(L57-L60) h (\(2000\)) 486 4121 y(Kolmogoro) n(v) 18 b(A.N.:) p Fa 19 w(On) f(the) h(conserv) l(ation) h(of) g(conditionally) h(p) r(erio) r(dic) f(motions) f(under) g(small) 602 4212 y(p) r(erturbation) 25 b(of) i(the) e(Hamiltonian) p Fr(,) h(Dokl.) g(Ak) l(ad.) f(Nauk.) g (SSR) p Fs 24 w(98) p Fr(,) h(469) h(\(1954\)) 486 4303 y(Moser) 36 b(J.:) p Fa 36 w(On) f(in) n(v) l(arian) n(t) g(curv) n(es) g(of) h(area-preserving) g(mappings) f(of) h(an) f(ann) n(ulus) p Fr(,) g(Nac) n(h.) 602 4394 y(Ak) l(ad.) 25 b(Wiss.) h(G\177) -38 b(ottingen,) 27 b(Math.) f(Ph) n(ys.) g(Kl.) g(I) r(I) p Fs 25 w(1) p Fr(,) g(1) g(\(1962\)) 486 4485 y(P) n(oincar) n(\023) -36 b(e) 32 b(H.:) p Fa 30 w(Les) g(M) n(\023) -36 b(etho) r(des) 31 b(Nouv) n(elles) g(de) g(la) g(M) n(\023) -36 b(ec) n(hanique) 31 b(C) n(\023) -36 b(eleste) p Fr(,) 32 b(Gauthier) f(Villars,) 602 4576 y(P) n(aris) c(\(1892\)) 486 4667 y(Ro) n(y) h(A.E.,) i(Ov) n (enden) e(M.W.:) p Fa 31 w(On) g(the) h(o) r(ccurrence) h(of) g (commensurable) e(mean) h(motions) g(in) 602 4758 y(the) h(Solar) i (System.) d(I) r(I) h(The) h(mirror) g(theorem) p Fr(,) f(Mon.) h(Not.) g(R.) f(astron.) i(So) r(c.) p Fs 31 w(115) p Fr(,) g(296) 602 4848 y(\(1955\)) p Fn 1902 5847 a(cchv-r5.tex;) 42 b(27/09/2001;) g (9:54;) e(p.17) p 90 rotate dyy eop %%Page: 18 18 18 17 bop Fv 486 100 a(18) p Fr 486 291 a(Szeb) r(ehely) 25 b(V.:) p Fa 26 w(Theory) g(of) i(orbits) p Fr(,) f(Academic) f(Press,) i (New) f(Y) -6 b(ork) 25 b(and) g(London) h(\(1967\)) 486 381 y(V) -6 b(alsecc) n(hi) 29 b(G.B.,) i(P) n(erozzi) g(E.,) f(Ro) n (y) e(A.E.,) i(Stev) n(es) f(B.A.:) p Fa 30 w(P) n(erio) r(dic) i (orbits) e(close) i(to) e(that) g(of) 602 472 y(the) c(Mo) r(on) p Fr(,) i(Astron.) f(Astroph) n(ys.) p Fs 25 w(271) p Fr(,) g(308-314) i (\(1993\)) 486 563 y(Win) n(ter) 21 b(O.C.,) h(Murra) n(y) f(C.D.:) p Fa 22 w(Resonance) h(and) f(Chaos.) i(I.) e(First-order) h(in) n (terior) g(resonances) p Fr(,) 602 654 y(Astron.) k(Astroph) n(ys.) p Fs 25 w(319) p Fr(,) g(290-304) i(\(1997\)) 486 745 y(Win) n(ter) 41 b(O.C.,) h(Murra) n(y) f(C.D.:) p Fa 42 w(Resonance) h(and) f(Chaos.) h (I) r(I.) f(Exterior) h(resonances) g(and) 602 836 y(asymmetric) 24 b(libration) p Fr(,) j(Astron.) f(Astroph) n(ys.) p Fs 25 w(328) p Fr(,) h(399-408) g(\(1997\)) g(Z) 486 927 y(Zuc) n(k) n(er) c(S.,) i(Mazeh) h(T.:) p Fa 26 w(Analysis) f(of) g (the) g(Hipparcos) g(measurmen) n(ts) e(of) j(HD10697) g(-) e(A) g (mass) 602 1018 y(determination) h(of) h(a) g(bro) n(wn-dw) n(arf) h (secondary) p Fr(,) f(Astroph) n(ys.) f(J.) p Fs 26 w(531) p Fr(,) i(L67-L69) g(\(2000\)) p Fn 1902 5847 a(cchv-r5.tex;) 42 b(27/09/2001;) g(9:54;) e(p.18) p 90 rotate dyy eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF