Content-Type: multipart/mixed; boundary="-------------0012230422929" This is a multi-part message in MIME format. ---------------0012230422929 Content-Type: text/plain; name="00-514.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="00-514.keywords" Hamiltonian systems -- Stability -- Perturbations -- Normal forms. ---------------0012230422929 Content-Type: application/postscript; name="Art-steep.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Art-steep.ps" 5 543 y Fc(k)99 531 y Fm(and)j(the)h(ma)s(joring)d(of)j Fl(\034)584 538 y Fk(l)599 531 y Fm(,)g(the)f(inequalit)o(y)g Fl("T)1014 500 y Fh(2)p Fk(\031)1057 505 y Fc(l)1072 500 y Fk(=\031)1115 505 y Fc(j)1130 514 y(k)1007 545 y Fk(j)1023 550 y Fc(k)1157 531 y Fl(K)j(<)-6 b Fg(\003)19 b Fm(\()p Fl(c)1339 538 y Fh(0)1361 531 y Fl(")1384 513 y Fk(a)1408 531 y Fm(\))1427 513 y Fk(\031)1450 518 y Fc(l)1487 531 y Fm(implies)f(the)i(threshold)0 601 y(\()p Fl(i)p Fm(\),)d(since)f 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Fg(\003)h Fm(1)f(for)h(an)o(y)f Fl(l)i Fg(2)f(f)p Fm(0)p Fl(;)8 b(:)g(:)g(:)g(;)g(n)14 b Fg(\000)g Fm(1)p Fg(g)20 b Fm(then)h(the)g(radii)e Fl(r)1253 1821 y Fk(l)1290 1814 y Fm(are)h(b)q(ounded)f(b)o(y)i Fd(e)-28 b Fl(c)1680 1821 y Fh(0)1702 1814 y Fl(")1725 1796 y Fk(a\031)1770 1801 y Fc(l)1808 1814 y Fm(with)20 b(a)0 1874 y(certain)c(p)q(ositiv)o (e)g(constan)o(t)g Fd(e)-28 b Fl(c)573 1881 y Fh(0)611 1874 y Fm(and)16 b(this)g(completes)g(the)h(pro)q(of)f(of)h(the)f (theorem)g(5.5.)21 b Fg(4)94 1993 y Fm(No)o(w,)e(w)o(e)g(can)g (complete)f(the)h(pro)q(of)f(of)h(the)g(main)f(result)g(\(theorem)g (2.1.\),)h(indeed)f(an)g(action)0 2053 y(can)13 b(drift)g(at)h(most)f (of)h(a)f(distance)g Fl(\032)683 2060 y Fk(l)711 2053 y Fm(at)h(eac)o(h)f(step)g(of)h(our)e(iterativ)o(e)i(pro)q(cess)e (\(with)i(the)g(lemmas)e(4.3.)0 2113 y(and)17 b(4.4.\))27 b(and)17 b(if)h Fl(\032)393 2120 y Fk(n)p Fj(\000)p Fh(1)487 2113 y Fg(\025)e Fl(")j Fm(an)e(action)h(can)g(drift)g(at)g(most)f(of)i (a)f(distance)f 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Fn(44)p Fm(,)h(pp.)21 b(153-182,)16 b(Springer-V)l(erlag)o(,)e(New-Y)l(ork,)i (1992.)0 1441 y([Il])f(Ily)o(ashenk)o(o,)g(I.S.)g(:)22 b(1986,)15 b(A)h(steepness)f(test)h(for)g(analytic)g(functions,)f Fi(R)o(ussian)j(Math.)23 b(Surveys)0 1501 y Fn(41)p Fm(,)16 b(pp.)21 b(229-230.)0 1581 y([L])i(Lo)q(c)o(hak,)h(P)l(.)e(:)35 b(1992,)23 b(Canonical)f(p)q(erturbation)f(theory)i(via)g(sim)o (ultaneous)d(appro)o(ximation,)0 1641 y Fi(R)o(ussian)f(Math.)k (Surveys)17 b Fn(47)p Fm(,)e(pp.)22 b(57-133.)0 1721 y([LMS])13 b(Lo)q(c)o(hak)h(P)l(.,)g(Marco)g(J.P)l(.,)f(Sauzin)g(D.)h (:)21 b(1999,)14 b(On)f(the)i(splitting)e(of)h(the)g(in)o(v)m(arian)o (t)f(manifolds)0 1781 y(in)h(m)o(ultidimensional)d(near-in)o(tegrable)h (Hamiltonioan)i(systems,)g Fi(Pr)o(\023)-24 b(e)16 b(public)m(ation)h (de)f(l'Institut)g(de)0 1841 y(Math)o(\023)-24 b(ematique)17 b(de)h(Jussieu)p Fm(,)f Fn(220)f Fm(\(Sept.)22 b(1999\).)0 1921 y([N1])17 b(Nekhoro)q(c)o(hev,)g(N.N.)h(:)24 b(1973,)17 b(Stable)f(lo)o(w)o(er)g(estimates)h(for)g(smo)q(oth)g(mappings)e(and)h (for)h(gra-)0 1981 y(dien)o(ts)e(of)i(smo)q(oth)f(functions,)f Fi(Math.)24 b(USSR)18 b(Sb)m(ornik)f Fn(19)p Fm(\(3\),)f(pp.)22 b(425-467.)0 2061 y([N2])17 b(Nekhoro)q(c)o(hev,)f(N.N.)h(:)22 b(1977,)17 b(An)f(exp)q(onen)o(tial)g(estimate)h(of)g(the)g(time)f(of)h (stabilit)o(y)f(of)h(nearly)0 2121 y(in)o(tegrable)e(Hamiltonian)g (systems,)h Fi(R)o(ussian)j(Math.)k(Surveys)16 b Fn(32)p Fm(,)g(pp.)21 b(1-65.)0 2201 y([N3])c(Nekhoro)q(c)o(hev,)f(N.N.)h(:)22 b(1979,)17 b(An)f(exp)q(onen)o(tial)g(estimate)h(of)g(the)g(time)f(of)h (stabilit)o(y)f(of)h(nearly)0 2261 y(in)o(tegrable)e(Hamiltonian)h (systems)g(2,)g Fi(T)l(rudy)i(Sem.)24 b(Petr)m(ovs)17 b Fn(5)p Fm(,)f(pp.)22 b(5-50,)16 b(translated)g(in)g(Oleinik,)0 2321 y(O.A.)d(\(Ed.\),)h(T)l(opics)e(in)h(Mo)q(dern)f(Mathematics,)h(P) o(etro)o(vskii)f(Semin.)19 b(\()p Fn(5)p Fm(\),)14 b(New)g(Y)l(ork)f(:) 21 b(Consultan)o(t)0 2380 y(Bureau)16 b(1985.)0 2461 y([Ni])j(Niederman,)e(L.)i(:)27 b(1998,)18 b(Nonlinear)g(stabilit)o(y)g (around)f(an)h(elliptic)h(equilibrium)d(p)q(oin)o(t)i(in)g(an)0 2520 y(Hamiltonian)d(system,)h Fi(Nonline)m(arity)i Fn(11)p Fm(,)d(pp.)22 b(1465-1479.)0 2601 y([P\177)-25 b(o])23 b(P\177)-25 b(osc)o(hel,)24 b(J.)f(:)35 b(1993,)25 b(Nekhoro)q(c)o(hev) e(estimates)g(for)g(quasi-con)o(v)o(ex)f(Hamiltonian)g(systems,)0 2660 y Fi(Math.)h(Z.)17 b Fn(213)p Fm(,)e(pp.)21 b(187-217.)950 2789 y(16)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0012230422929--