Content-Type: multipart/mixed; boundary="-------------0201150459879" This is a multi-part message in MIME format. ---------------0201150459879 Content-Type: text/plain; name="02-21.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="02-21.keywords" Bogdanov-Takens bifurcation, homoclinic orbits, exponentially small phenomena ---------------0201150459879 Content-Type: application/x-tex; name="mp_arc_Jan_2002.tex" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="mp_arc_Jan_2002.tex" % This TeX file was generated by ./texpsinclude % from the original TeX file gelfreich_mp_arc_2002.tex % and the PostScript files gelfreich_fig_1.eps gelfreich_fig_2.eps. % TeX writes out the included PostScript to files. % % Here is part of gelfreich_mp_arc_2002.tex: \documentclass[12pt]{article} % Here are the % TeX macros for dumping included Postscript to files. % Adapted from Knuth's \answer macro in the TeXbook. % Jamie Stephens, jamies@math.utexas.edu, 28 Nov 94 \def\endofps{EndOfTheIncludedPostscriptMagicCookie} \chardef\other=12 \newwrite\psdumphandle \outer\def\psdump#1{\par\medbreak \immediate\openout\psdumphandle=#1 \copytoblankline} \def\copytoblankline{\begingroup\setupcopy\copypsline} \def\setupcopy{\def\do##1{\catcode`##1=\other}\dospecials \catcode`\\=\other \obeylines} {\obeylines \gdef\copypsline#1 {\def\next{#1}% \ifx\next\endofps\let\next=\endgroup % \else\immediate\write\psdumphandle{\next} \let\next=\copypsline\fi\next}} \outer\def\closepsdump{ \immediate\closeout\psdumphandle} % Here is the PostScript for gelfreich_fig_1.eps: \message{Writing file gelfreich_fig_1.eps} \psdump{gelfreich_fig_1.eps} %!PS-Adobe-3.0 EPSF-3.0 %%Creator: Adobe Illustrator(R) 8.0 %%AI8_CreatorVersion: 8 %%For: (x y) (FU-Berlin) %%Title: (gelfreich_fig_1.eps) %%CreationDate: (1/2/02) (3:44 PM) %%BoundingBox: 133 683 283 799 %%HiResBoundingBox: 133.8706 683.6128 282.439 798.0713 %%DocumentProcessColors: Black %%DocumentFonts: Symbol %%+ Times-Roman %%DocumentSuppliedFonts: Symbol %%+ Times-Roman %%DocumentSuppliedResources: procset Adobe_level2_AI5 1.2 0 %%+ procset Adobe_typography_AI5 1.0 1 %%+ procset Adobe_ColorImage_AI6 1.3 0 %%+ procset Adobe_Illustrator_AI5 1.3 0 %%+ procset Adobe_cshow 2.0 8 %%+ procset Adobe_shading_AI8 1.0 0 %AI5_FileFormat 4.0 %AI3_ColorUsage: Black&White %AI3_IncludePlacedImages %AI7_ImageSettings: 1 %%CMYKProcessColor: 1 1 1 1 ([Passermarken]) %%AI6_ColorSeparationSet: 1 1 (AI6 Default Color Separation Set) %%+ Options: 1 16 0 1 0 1 1 1 0 1 1 1 1 8.504 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 2 3 4 %%+ PPD: 1 21 0 0 60 45 2 2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 () %AI3_TemplateBox: 297.5 420.5 297.5 420.5 %AI3_TileBox: 14 13 581 830 %AI3_DocumentPreview: Header %AI5_ArtSize: 595 842 %AI5_RulerUnits: 2 %AI5_ArtFlags: 1 0 0 1 0 0 1 0 0 %AI5_TargetResolution: 800 %AI5_NumLayers: 1 %AI8_OpenToView: 109.752 844.7437 5.1756 953 693 18 0 1 11 68 0 0 %AI5_OpenViewLayers: 7 %%PageOrigin:14 13 %%AI3_PaperRect:-14 830 581 -12 %%AI3_Margin:14 -13 -14 12 %AI7_GridSettings: 72 8 72 8 1 0 0.8 0.8 0.8 0.9 0.9 0.9 %%EndComments %%BeginProlog %%BeginResource: procset Adobe_level2_AI5 1.2 0 %%Title: (Adobe Illustrator (R) Version 5.0 Level 2 Emulation) %%Version: 1.2 0 %%CreationDate: (04/10/93) () %%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved) userdict /Adobe_level2_AI5 26 dict dup begin put /packedarray where not { userdict begin /packedarray { array astore readonly } bind def /setpacking /pop load def /currentpacking false def end 0 } if pop userdict /defaultpacking currentpacking put true setpacking /initialize { Adobe_level2_AI5 begin } bind def /terminate { currentdict Adobe_level2_AI5 eq { end } if } bind def mark /setcustomcolor where not { /findcmykcustomcolor { (AI8_CMYK_CustomColor) 6 packedarray } bind def /findrgbcustomcolor { (AI8_RGB_CustomColor) 5 packedarray } bind def /setcustomcolor { exch aload pop dup (AI8_CMYK_CustomColor) eq { pop pop 4 { 4 index mul 4 1 roll } repeat 5 -1 roll pop setcmykcolor } { dup (AI8_RGB_CustomColor) eq { pop pop 3 { 1 exch sub 3 index mul 1 exch sub 3 1 roll } repeat 4 -1 roll pop setrgbcolor } { pop 4 { 4 index mul 4 1 roll } repeat 5 -1 roll pop setcmykcolor } ifelse } ifelse } def } if /setAIseparationgray { false setoverprint 0 setgray /setseparationgray where{ pop setseparationgray }{ /setcolorspace where{ pop [/Separation (All) /DeviceCMYK {dup dup dup}] setcolorspace 1 exch sub setcolor }{ setgray }ifelse }ifelse } def /gt38? mark {version cvr cvx exec} stopped {cleartomark true} {38 gt exch pop} ifelse def userdict /deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt put userdict /level2? systemdict /languagelevel known dup { pop systemdict /languagelevel get 2 ge } if put /level2ScreenFreq { begin 60 HalftoneType 1 eq { pop Frequency } if HalftoneType 2 eq { pop GrayFrequency } if HalftoneType 5 eq { pop Default level2ScreenFreq } if end } bind def userdict /currentScreenFreq level2? {currenthalftone level2ScreenFreq} {currentscreen pop pop} ifelse put level2? not { /setcmykcolor where not { /setcmykcolor { exch .11 mul add exch .59 mul add exch .3 mul add 1 exch sub setgray } def } if /currentcmykcolor where not { /currentcmykcolor { 0 0 0 1 currentgray sub } def } if /setoverprint where not { /setoverprint /pop load def } if /selectfont where not { /selectfont { exch findfont exch dup type /arraytype eq { makefont } { scalefont } ifelse setfont } bind def } if /cshow where not { /cshow { [ 0 0 5 -1 roll aload pop ] cvx bind forall } bind def } if } if cleartomark /anyColor? { add add add 0 ne } bind def /testColor { gsave setcmykcolor currentcmykcolor grestore } bind def /testCMYKColorThrough { testColor anyColor? } bind def userdict /composite? 1 0 0 0 testCMYKColorThrough 0 1 0 0 testCMYKColorThrough 0 0 1 0 testCMYKColorThrough 0 0 0 1 testCMYKColorThrough and and and put composite? not { userdict begin gsave /cyan? 1 0 0 0 testCMYKColorThrough def /magenta? 0 1 0 0 testCMYKColorThrough def /yellow? 0 0 1 0 testCMYKColorThrough def /black? 0 0 0 1 testCMYKColorThrough def grestore /isCMYKSep? cyan? magenta? yellow? black? or or or def /customColor? isCMYKSep? not def end } if end defaultpacking setpacking %%EndResource %%BeginResource: procset Adobe_typography_AI5 1.0 1 %%Title: (Typography Operators) %%Version: 1.0 1 %%CreationDate:(6/10/1996) () %%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_typography_AI5 68 dict dup begin put /initialize { begin begin Adobe_typography_AI5 begin Adobe_typography_AI5 { dup xcheck { bind } if pop pop } forall end end end Adobe_typography_AI5 begin } def /terminate { currentdict Adobe_typography_AI5 eq { end } if } def /modifyEncoding { /_tempEncode exch ddef /_pntr 0 ddef { counttomark -1 roll dup type dup /marktype eq { pop pop exit } { /nametype eq { _tempEncode /_pntr dup load dup 3 1 roll 1 add ddef 3 -1 roll put } { /_pntr exch ddef } ifelse } ifelse } loop _tempEncode } def /havefont { systemdict /languagelevel known { /Font resourcestatus dup { exch pop exch pop } if } { systemdict /FontDirectory get 1 index known { pop true } { systemdict /fileposition known { dup length 6 add exch Ss 6 250 getinterval cvs pop Ss exch 0 exch getinterval status { pop pop pop pop true } { false } ifelse } { pop false } ifelse } ifelse } ifelse } def /TE { StandardEncoding 256 array copy modifyEncoding /_nativeEncoding exch def } def /subststring { exch 2 index exch search { exch pop exch dup () eq { pop exch concatstring } { 3 -1 roll exch concatstring concatstring } ifelse exch pop true } { pop pop false } ifelse } def /concatstring { 1 index length 1 index length 1 index add string dup 0 5 index putinterval dup 2 index 4 index putinterval 4 1 roll pop pop pop } def % /TZ { dup type /arraytype eq { /_wv exch def } { /_wv 0 def } ifelse /_useNativeEncoding exch def 2 index havefont { 3 index 255 string cvs dup (_Symbol_) eq { pop 2 index findfont } { 1 index 0 eq { dup length 1 sub 1 exch getinterval cvn findfont } { pop 2 index findfont } ifelse } ifelse } { dup 1 eq { 2 index 64 string cvs dup (-90pv-RKSJ-) (-83pv-RKSJ-) subststring { exch pop dup havefont { findfont false } { pop true } ifelse } { pop dup (-90ms-RKSJ-) (-Ext-RKSJ-) subststring { exch pop dup havefont { findfont false } { pop true } ifelse } { pop pop true } ifelse } ifelse { 1 index 1 eq { /Ryumin-Light-Ext-RKSJ-V havefont {/Ryumin-Light-Ext-RKSJ-V} {/Courier} ifelse } { /Ryumin-Light-83pv-RKSJ-H havefont {/Ryumin-Light-83pv-RKSJ-H} {/Courier} ifelse } ifelse findfont [1 0 0.5 1 0 0] makefont } if } { /Courier findfont } ifelse } ifelse _wv type /arraytype eq { _wv makeblendedfont } if dup length 10 add dict begin mark exch { 1 index /FID ne { def } if cleartomark mark } forall pop /FontScript exch def /FontDirection exch def /FontRequest exch def /FontName exch def counttomark 0 eq { 1 _useNativeEncoding eq { /Encoding _nativeEncoding def } if cleartomark } { /Encoding load 256 array copy modifyEncoding /Encoding exch def } ifelse FontName currentdict end definefont pop } def /tr { _ax _ay 3 2 roll } def /trj { _cx _cy _sp _ax _ay 6 5 roll } def /a0 { /Tx { dup currentpoint 3 2 roll tr _psf newpath moveto tr _ctm _pss } ddef /Tj { dup currentpoint 3 2 roll trj _pjsf newpath moveto trj _ctm _pjss } ddef } def /a1 { W B } def /e0 { /Tx { tr _psf } ddef /Tj { trj _pjsf } ddef } def /e1 { W F } def /i0 { /Tx { tr sp } ddef /Tj { trj jsp } ddef } def /i1 { W N } def /o0 { /Tx { tr sw rmoveto } ddef /Tj { trj swj rmoveto } ddef } def /r0 { /Tx { tr _ctm _pss } ddef /Tj { trj _ctm _pjss } ddef } def /r1 { W S } def /To { pop _ctm currentmatrix pop } def /TO { iTe _ctm setmatrix newpath } def /Tp { pop _tm astore pop _ctm setmatrix _tDict begin /W { } def /h { } def } def /TP { end iTm 0 0 moveto } def /Tr { _render 3 le { currentpoint newpath moveto } if dup 8 eq { pop 0 } { dup 9 eq { pop 1 } if } ifelse dup /_render exch ddef _renderStart exch get load exec } def /iTm { _ctm setmatrix _tm concat _shift aload pop _lineorientation 1 eq { exch } if translate _scale aload pop _lineorientation 1 eq _yokoorientation 1 eq or { exch } if scale } def /Tm { _tm astore pop iTm 0 0 moveto } def /Td { _mtx translate _tm _tm concatmatrix pop iTm 0 0 moveto } def /iTe { _render -1 eq { } { _renderEnd _render get dup null ne { load exec } { pop } ifelse } ifelse /_render -1 ddef } def /Ta { pop } def /Tf { 1 index type /nametype eq { dup 0.75 mul 1 index 0.25 mul neg } if /_fontDescent exch ddef /_fontAscent exch ddef /_fontSize exch ddef /_fontRotateAdjust _fontAscent _fontDescent add 2 div neg ddef /_fontHeight _fontSize ddef findfont _fontSize scalefont setfont } def /Tl { pop neg 0 exch _leading astore pop } def /Tt { pop } def /TW { 3 npop } def /Tw { /_cx exch ddef } def /TC { 3 npop } def /Tc { /_ax exch ddef } def /Ts { 0 exch _shift astore pop currentpoint iTm moveto } def /Ti { 3 npop } def /Tz { count 1 eq { 100 } if 100 div exch 100 div exch _scale astore pop iTm } def /TA { pop } def /Tq { pop } def /Tg { pop } def /TG { pop } def /Tv { /_lineorientation exch ddef } def /TV { /_charorientation exch ddef } def /Ty { dup /_yokoorientation exch ddef 1 sub neg Tv } def /TY { pop } def /T~ { Tx } def /Th { pop pop pop pop pop } def /TX { pop } def /Tk { _fontSize mul 1000 div _lineorientation 0 eq { neg 0 } { 0 exch } ifelse rmoveto pop } def /TK { 2 npop } def /T* { _leading aload pop _lineorientation 0 ne { exch } if Td } def /T*- { _leading aload pop _lineorientation 0 ne { exch } if exch neg exch neg Td } def /T- { _ax neg 0 rmoveto _lineorientation 1 eq _charorientation 0 eq and { 1 TV _hyphen Tx 0 TV } { _hyphen Tx } ifelse } def /T+ { } def /TR { _ctm currentmatrix pop _tm astore pop iTm 0 0 moveto } def /TS { currentfont 3 1 roll /_Symbol_ findfont _fontSize scalefont setfont 0 eq { Tx } { Tj } ifelse setfont } def /Xb { pop pop } def /Tb /Xb load def /Xe { pop pop pop pop } def /Te /Xe load def /XB { } def /TB /XB load def currentdict readonly pop end setpacking % /X^ { currentfont 5 1 roll dup havefont { findfont _fontSize scalefont setfont } { pop exch } ifelse 2 index 0 eq { Tx } { Tj } ifelse pop pop setfont } def /T^ /X^ load def %%EndResource %%BeginProcSet: Adobe_ColorImage_AI6 1.3 0 userdict /Adobe_ColorImage_AI6 known not { userdict /Adobe_ColorImage_AI6 53 dict put } if userdict /Adobe_ColorImage_AI6 get begin /initialize { Adobe_ColorImage_AI6 begin Adobe_ColorImage_AI6 { dup type /arraytype eq { dup xcheck { bind } if } if pop pop } forall } def /terminate { end } def currentdict /Adobe_ColorImage_AI6_Vars known not { /Adobe_ColorImage_AI6_Vars 41 dict def } if Adobe_ColorImage_AI6_Vars begin /plateindex -1 def /_newproc null def /_proc1 null def /_proc2 null def /sourcearray 4 array def /_ptispace null def /_ptiname null def /_pti0 0 def /_pti1 0 def /_ptiproc null def /_ptiscale 0 def /_pticomps 0 def /_ptibuf 0 string def /_gtigray 0 def /_cticmyk null def /_rtirgb null def /XIEnable true def /XIType 0 def /XIEncoding 0 def /XICompression 0 def /XIChannelCount 0 def /XIBitsPerPixel 0 def /XIImageHeight 0 def /XIImageWidth 0 def /XIImageMatrix null def /XIRowBytes 0 def /XIFile null def /XIBuffer1 null def /XIBuffer2 null def /XIBuffer3 null def /XIDataProc null def /XIColorSpace /DeviceGray def /XIColorValues 0 def /XIPlateList false def end /ci6colorimage /colorimage where {/colorimage get}{null} ifelse def /ci6image systemdict /image get def /ci6curtransfer systemdict /currenttransfer get def /ci6curoverprint /currentoverprint where {/currentoverprint get}{{_of}} ifelse def /ci6foureq { 4 index ne { pop pop pop false }{ 4 index ne { pop pop false }{ 4 index ne { pop false }{ 4 index eq } ifelse } ifelse } ifelse } def /ci6testplate { Adobe_ColorImage_AI6_Vars begin /plateindex -1 def /setcmykcolor where { pop gsave 1 0 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub 0 1 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub 0 0 1 0 setcmykcolor systemdict /currentgray get exec 1 exch sub 0 0 0 1 setcmykcolor systemdict /currentgray get exec 1 exch sub grestore 1 0 0 0 ci6foureq { /plateindex 0 def }{ 0 1 0 0 ci6foureq { /plateindex 1 def }{ 0 0 1 0 ci6foureq { /plateindex 2 def }{ 0 0 0 1 ci6foureq { /plateindex 3 def }{ 0 0 0 0 ci6foureq { /plateindex 5 def } if } ifelse } ifelse } ifelse } ifelse pop pop pop pop } if plateindex end } def /ci6concatprocs { /packedarray where { pop dup type /packedarraytype eq 2 index type /packedarraytype eq or }{ false } ifelse { /_proc2 exch cvlit def /_proc1 exch cvlit def _proc1 aload pop _proc2 aload pop _proc1 length _proc2 length add packedarray cvx }{ /_proc2 exch cvlit def /_proc1 exch cvlit def /_newproc _proc1 length _proc2 length add array def _newproc 0 _proc1 putinterval _newproc _proc1 length _proc2 putinterval _newproc cvx } ifelse } def /ci6istint { type /arraytype eq } def /ci6isspot { dup type /arraytype eq { dup length 1 sub get /Separation eq }{ pop false } ifelse } def /ci6spotname { dup ci6isspot {dup length 2 sub get}{pop ()} ifelse } def /ci6altspace { aload pop pop pop ci6colormake } def /ci6numcomps { dup /DeviceGray eq { pop 1 }{ dup /DeviceRGB eq { pop 3 }{ /DeviceCMYK eq { 4 }{ 1 } ifelse } ifelse } ifelse } def /ci6marksplate { dup /DeviceGray eq { pop plateindex 3 eq }{ dup /DeviceRGB eq { pop plateindex 5 ne }{ dup /DeviceCMYK eq { pop plateindex 5 ne }{ dup ci6isspot { /findcmykcustomcolor where { pop dup length 2 sub get 0.1 0.1 0.1 0.1 5 -1 roll findcmykcustomcolor 1 setcustomcolor systemdict /currentgray get exec 1 ne }{ pop plateindex 5 ne } ifelse }{ pop plateindex 5 ne } ifelse } ifelse } ifelse } ifelse } def /ci6colormake { dup ci6numcomps exch 1 index 2 add 1 roll dup 1 eq {pop}{array astore} ifelse exch } def /ci6colorexpand { dup ci6spotname exch dup ci6istint { ci6altspace exch 4 1 roll }{ 1 3 1 roll } ifelse } def /ci6colortint { dup /DeviceGray eq { 3 1 roll 1 exch sub mul 1 exch sub exch }{ dup /DeviceRGB eq { 3 1 roll {1 exch sub 1 index mul 1 exch sub exch} forall pop 3 array astore exch }{ dup /DeviceCMYK eq { 3 1 roll {1 index mul exch} forall pop 4 array astore exch }{ 3 1 roll mul exch } ifelse } ifelse } ifelse } def /ci6colortocmyk { dup /DeviceGray eq { pop 1 exch sub 0 0 0 4 -1 roll 4 array astore }{ dup /DeviceRGB eq { pop aload pop _rgbtocmyk 4 array astore }{ dup /DeviceCMYK eq { pop }{ ci6altspace ci6colortint ci6colortocmyk } ifelse } ifelse } ifelse } def /ci6makeimagedict { 7 dict begin /ImageType 1 def /Decode exch def /DataSource exch def /ImageMatrix exch def /BitsPerComponent exch def /Height exch def /Width exch def currentdict end } def /ci6stringinvert { 0 1 2 index length 1 sub { dup 2 index exch get 255 exch sub 2 index 3 1 roll put } for } def /ci6stringknockout { 0 1 2 index length 1 sub { 255 2 index 3 1 roll put } for } def /ci6stringapply { 0 1 4 index length 1 sub { dup 4 index exch get 3 index 3 1 roll 3 index exec } for pop exch pop } def /ci6walkrgbstring { 0 3 index dup length 1 sub 0 3 3 -1 roll { 3 getinterval {} forall 5 index exec 3 index } for 5 {pop} repeat } def /ci6walkcmykstring { 0 3 index dup length 1 sub 0 4 3 -1 roll { 4 getinterval {} forall 6 index exec 3 index } for 5 { pop } repeat } def /ci6putrgbtograystr { .11 mul exch .59 mul add exch .3 mul add cvi 3 copy put pop 1 add } def /ci6putcmyktograystr { exch .11 mul add exch .59 mul add exch .3 mul add dup 255 gt { pop 255 } if 255 exch sub cvi 3 copy put pop 1 add } def /ci6rgbtograyproc { Adobe_ColorImage_AI6_Vars begin sourcearray 0 get exec XIBuffer3 dup 3 1 roll /ci6putrgbtograystr load exch ci6walkrgbstring end } def /ci6cmyktograyproc { Adobe_ColorImage_AI6_Vars begin sourcearray 0 get exec XIBuffer3 dup 3 1 roll /ci6putcmyktograystr load exch ci6walkcmykstring end } def /ci6separatecmykproc { Adobe_ColorImage_AI6_Vars begin sourcearray 0 get exec XIBuffer3 0 2 index plateindex 4 2 index length 1 sub { get 255 exch sub 3 copy put pop 1 add 2 index } for pop pop exch pop end } def /ci6compositeimage { dup 1 eq { pop pop image }{ /ci6colorimage load null ne { ci6colorimage }{ 3 1 roll pop sourcearray 0 3 -1 roll put 3 eq {/ci6rgbtograyproc}{/ci6cmyktograyproc} ifelse load image } ifelse } ifelse } def /ci6knockoutimage { gsave 0 ci6curtransfer exec 1 ci6curtransfer exec eq { 0 ci6curtransfer exec 0.5 lt }{ 0 ci6curtransfer exec 1 ci6curtransfer exec gt } ifelse {{pop 0}}{{pop 1}} ifelse systemdict /settransfer get exec ci6compositeimage grestore } def /ci6drawimage { ci6testplate -1 eq { pop ci6compositeimage }{ dup type /arraytype eq { dup length plateindex gt {plateindex get}{pop false} ifelse }{ { true }{ dup 1 eq {plateindex 3 eq}{plateindex 3 le} ifelse } ifelse } ifelse { dup 1 eq { pop pop ci6image }{ dup 3 eq { ci6compositeimage }{ pop pop sourcearray 0 3 -1 roll put /ci6separatecmykproc load ci6image } ifelse } ifelse }{ ci6curoverprint { 7 {pop} repeat }{ ci6knockoutimage } ifelse } ifelse } ifelse } def /ci6proctintimage { /_ptispace exch store /_ptiname exch store /_pti1 exch store /_pti0 exch store /_ptiproc exch store /_pticomps _ptispace ci6numcomps store /_ptiscale _pti1 _pti0 sub store level2? { _ptiname length 0 gt version cvr 2012 ge and { [/Separation _ptiname _ptispace {_ptiproc}] setcolorspace [_pti0 _pti1] ci6makeimagedict ci6image }{ [/Indexed _ptispace 255 {255 div _ptiscale mul _pti0 add _ptiproc}] setcolorspace [0 255] ci6makeimagedict ci6image } ifelse }{ _pticomps 1 eq { { dup { 255 div _ptiscale mul _pti0 add _ptiproc 255 mul cvi put } ci6stringapply } ci6concatprocs ci6image }{ { dup length _pticomps mul dup _ptibuf length ne {/_ptibuf exch string store}{pop} ifelse _ptibuf { exch _pticomps mul exch 255 div _ptiscale mul _pti0 add _ptiproc _pticomps 2 add -2 roll _pticomps 1 sub -1 0 { 1 index add 2 index exch 5 -1 roll 255 mul cvi put } for pop pop } ci6stringapply } ci6concatprocs false _pticomps /ci6colorimage load null eq {7 {pop} repeat}{ci6colorimage} ifelse } ifelse } ifelse } def /ci6graytintimage { /_gtigray 5 -1 roll store {1 _gtigray sub mul 1 exch sub} 4 1 roll /DeviceGray ci6proctintimage } def /ci6cmyktintimage { /_cticmyk 5 -1 roll store {_cticmyk {1 index mul exch} forall pop} 4 1 roll /DeviceCMYK ci6proctintimage } def /ci6rgbtintimage { /_rtirgb 5 -1 roll store {_rtirgb {1 exch sub 1 index mul 1 exch sub exch} forall pop} 4 1 roll /DeviceRGB ci6proctintimage } def /ci6tintimage { ci6testplate -1 eq { ci6colorexpand 3 -1 roll 5 -1 roll {0}{0 exch} ifelse 4 2 roll dup /DeviceGray eq { pop ci6graytintimage }{ dup /DeviceRGB eq { pop ci6rgbtintimage }{ pop ci6cmyktintimage } ifelse } ifelse }{ dup ci6marksplate { plateindex 5 lt { ci6colortocmyk plateindex get dup 0 eq ci6curoverprint and { 7 {pop} repeat }{ 1 exch sub exch {1 0}{0 1} ifelse () ci6graytintimage } ifelse }{ pop exch {0}{0 exch} ifelse 0 3 1 roll () ci6graytintimage } ifelse }{ ci6curoverprint { 8 {pop} repeat }{ pop pop pop {pop 1} 0 1 () /DeviceGray ci6proctintimage } ifelse } ifelse } ifelse } def /XINullImage { } def /XIImageMask { XIImageWidth XIImageHeight false [XIImageWidth 0 0 XIImageHeight neg 0 0] /XIDataProc load imagemask } def /XIImageTint { XIImageWidth XIImageHeight XIBitsPerPixel [XIImageWidth 0 0 XIImageHeight neg 0 0] /XIDataProc load XIType 3 eq XIColorValues XIColorSpace ci6tintimage } def /XIImage { XIImageWidth XIImageHeight XIBitsPerPixel [XIImageWidth 0 0 XIImageHeight neg 0 0] /XIDataProc load false XIChannelCount XIPlateList ci6drawimage } def /XG { pop pop } def /XF { 13 {pop} repeat } def /Xh { Adobe_ColorImage_AI6_Vars begin gsave /XIType exch def /XIImageHeight exch def /XIImageWidth exch def /XIImageMatrix exch def 0 0 moveto XIImageMatrix concat XIImageWidth XIImageHeight scale /_lp /null ddef _fc /_lp /imagemask ddef end } def /XH { Adobe_ColorImage_AI6_Vars begin grestore end } def /XIEnable { Adobe_ColorImage_AI6_Vars /XIEnable 3 -1 roll put } def /XC { Adobe_ColorImage_AI6_Vars begin ci6colormake /XIColorSpace exch def /XIColorValues exch def end } def /XIPlates { Adobe_ColorImage_AI6_Vars begin /XIPlateList exch def end } def /XI { Adobe_ColorImage_AI6_Vars begin gsave /XIType exch def cvi dup 256 idiv /XICompression exch store 256 mod /XIEncoding exch store pop pop /XIChannelCount exch def /XIBitsPerPixel exch def /XIImageHeight exch def /XIImageWidth exch def pop pop pop pop /XIImageMatrix exch def XIBitsPerPixel 1 eq { XIImageWidth 8 div ceiling cvi }{ XIImageWidth XIChannelCount mul } ifelse /XIRowBytes exch def XIEnable { /XIBuffer3 XIImageWidth string def XICompression 0 eq { /XIBuffer1 XIRowBytes string def XIEncoding 0 eq { {currentfile XIBuffer1 readhexstring pop} }{ {currentfile XIBuffer1 readstring pop} } ifelse }{ /XIBuffer1 256 string def /XIBuffer2 XIRowBytes string def {currentfile XIBuffer1 readline pop (%) anchorsearch {pop} if} /ASCII85Decode filter /DCTDecode filter /XIFile exch def {XIFile XIBuffer2 readstring pop} } ifelse /XIDataProc exch def XIType 1 ne { 0 setgray } if XIType 1 eq { XIImageMask }{ XIType 2 eq XIType 3 eq or { XIImageTint }{ XIImage } ifelse } ifelse }{ XINullImage } ifelse /XIPlateList false def grestore end } def end %%EndProcSet %%BeginResource: procset Adobe_Illustrator_AI5 1.3 0 %%Title: (Adobe Illustrator (R) Version 8.0 Full Prolog) %%Version: 1.3 0 %%CreationDate: (3/7/1994) () %%Copyright: ((C) 1987-1998 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_Illustrator_AI5_vars 112 dict dup begin put /_?cmyk false def /_eo false def /_lp /none def /_pf { } def /_ps { } def /_psf { } def /_pss { } def /_pjsf { } def /_pjss { } def /_pola 0 def /_doClip 0 def /cf currentflat def /_lineorientation 0 def /_charorientation 0 def /_yokoorientation 0 def /_tm matrix def /_renderStart [ /e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0 ] def /_renderEnd [ null null null null /i1 /i1 /i1 /i1 ] def /_render -1 def /_shift [0 0] def /_ax 0 def /_ay 0 def /_cx 0 def /_cy 0 def /_leading [ 0 0 ] def /_ctm matrix def /_mtx matrix def /_sp 16#020 def /_hyphen (-) def /_fontSize 0 def /_fontAscent 0 def /_fontDescent 0 def /_fontHeight 0 def /_fontRotateAdjust 0 def /Ss 256 string def Ss 0 (fonts/) putinterval /_cnt 0 def /_scale [1 1] def /_nativeEncoding 0 def /_useNativeEncoding 0 def /_tempEncode 0 def /_pntr 0 def /_tDict 2 dict def /_hfname 100 string def /_hffound false def /Tx { } def /Tj { } def /CRender { } def /_AI3_savepage { } def /_gf null def /_cf 4 array def /_rgbf 3 array def /_if null def /_of false def /_fc { } def /_gs null def /_cs 4 array def /_rgbs 3 array def /_is null def /_os false def /_sc { } def /_pd 1 dict def /_ed 15 dict def /_pm matrix def /_fm null def /_fd null def /_fdd null def /_sm null def /_sd null def /_sdd null def /_i null def /_lobyte 0 def /_hibyte 0 def /_cproc null def /_cscript 0 def /_hvax 0 def /_hvay 0 def /_hvwb 0 def /_hvcx 0 def /_hvcy 0 def /_bitfont null def /_bitlobyte 0 def /_bithibyte 0 def /_bitkey null def /_bitdata null def /_bitindex 0 def /discardSave null def /buffer 256 string def /beginString null def /endString null def /endStringLength null def /layerCnt 1 def /layerCount 1 def /perCent (%) 0 get def /perCentSeen? false def /newBuff null def /newBuffButFirst null def /newBuffLast null def /clipForward? false def end userdict /Adobe_Illustrator_AI5 known not { userdict /Adobe_Illustrator_AI5 100 dict put } if userdict /Adobe_Illustrator_AI5 get begin /initialize { Adobe_Illustrator_AI5 dup begin Adobe_Illustrator_AI5_vars begin /_aicmykps where {pop /_?cmyk _aicmykps def}if discardDict { bind pop pop } forall dup /nc get begin { dup xcheck 1 index type /operatortype ne and { bind } if pop pop } forall end newpath } def /terminate { end end } def /_ null def /ddef { Adobe_Illustrator_AI5_vars 3 1 roll put } def /xput { dup load dup length exch maxlength eq { dup dup load dup length 2 mul dict copy def } if load begin def end } def /npop { { pop } repeat } def /hswj { dup stringwidth 3 2 roll { _hvwb eq { exch _hvcx add exch _hvcy add } if exch _hvax add exch _hvay add } cforall } def /vswj { 0 0 3 -1 roll { dup 255 le _charorientation 1 eq and { dup cstring stringwidth 5 2 roll _hvwb eq { exch _hvcy sub exch _hvcx sub } if exch _hvay sub exch _hvax sub 4 -1 roll sub exch 3 -1 roll sub exch } { _hvwb eq { exch _hvcy sub exch _hvcx sub } if exch _hvay sub exch _hvax sub _fontHeight sub } ifelse } cforall } def /swj { 6 1 roll /_hvay exch ddef /_hvax exch ddef /_hvwb exch ddef /_hvcy exch ddef /_hvcx exch ddef _lineorientation 0 eq { hswj } { vswj } ifelse } def /sw { 0 0 0 6 3 roll swj } def /vjss { 4 1 roll { dup cstring dup length 1 eq _charorientation 1 eq and { -90 rotate currentpoint _fontRotateAdjust add moveto gsave false charpath currentpoint 5 index setmatrix stroke grestore _fontRotateAdjust sub moveto _sp eq { 5 index 5 index rmoveto } if 2 copy rmoveto 90 rotate } { currentpoint _fontHeight sub 5 index sub 3 index _sp eq { 9 index sub } if currentpoint exch 4 index stringwidth pop 2 div sub exch _fontAscent sub moveto gsave 2 index false charpath 6 index setmatrix stroke grestore moveto pop pop } ifelse } cforall 6 npop } def /hjss { 4 1 roll { dup cstring gsave false charpath currentpoint 5 index setmatrix stroke grestore moveto _sp eq { 5 index 5 index rmoveto } if 2 copy rmoveto } cforall 6 npop } def /jss { _lineorientation 0 eq { hjss } { vjss } ifelse } def /ss { 0 0 0 7 3 roll jss } def /vjsp { 4 1 roll { dup cstring dup length 1 eq _charorientation 1 eq and { -90 rotate currentpoint _fontRotateAdjust add moveto false charpath currentpoint _fontRotateAdjust sub moveto _sp eq { 5 index 5 index rmoveto } if 2 copy rmoveto 90 rotate } { currentpoint _fontHeight sub 5 index sub 3 index _sp eq { 9 index sub } if currentpoint exch 4 index stringwidth pop 2 div sub exch _fontAscent sub moveto 2 index false charpath moveto pop pop } ifelse } cforall 6 npop } def /hjsp { 4 1 roll { dup cstring false charpath _sp eq { 5 index 5 index rmoveto } if 2 copy rmoveto } cforall 6 npop } def /jsp { matrix currentmatrix _lineorientation 0 eq {hjsp} {vjsp} ifelse } def /sp { matrix currentmatrix 0 0 0 7 3 roll _lineorientation 0 eq {hjsp} {vjsp} ifelse } def /pl { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } def /setstrokeadjust where { pop true setstrokeadjust /c { curveto } def /C /c load def /v { currentpoint 6 2 roll curveto } def /V /v load def /y { 2 copy curveto } def /Y /y load def /l { lineto } def /L /l load def /m { moveto } def } { /c { pl curveto } def /C /c load def /v { currentpoint 6 2 roll pl curveto } def /V /v load def /y { pl 2 copy curveto } def /Y /y load def /l { pl lineto } def /L /l load def /m { pl moveto } def } ifelse /d { setdash } def /cf { } def /i { dup 0 eq { pop cf } if setflat } def /j { setlinejoin } def /J { setlinecap } def /M { setmiterlimit } def /w { setlinewidth } def /XR { 0 ne /_eo exch ddef } def /H { } def /h { closepath } def /N { _pola 0 eq { _doClip 1 eq { _eo {eoclip} {clip} ifelse /_doClip 0 ddef } if newpath } { /CRender { N } ddef } ifelse } def /n { N } def /F { _pola 0 eq { _doClip 1 eq { gsave _pf grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _fc /_doClip 0 ddef } { _pf } ifelse } { /CRender { F } ddef } ifelse } def /f { closepath F } def /S { _pola 0 eq { _doClip 1 eq { gsave _ps grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc /_doClip 0 ddef } { _ps } ifelse } { /CRender { S } ddef } ifelse } def /s { closepath S } def /B { _pola 0 eq { _doClip 1 eq gsave F grestore { gsave S grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc /_doClip 0 ddef } { S } ifelse } { /CRender { B } ddef } ifelse } def /b { closepath B } def /W { /_doClip 1 ddef } def /* { count 0 ne { dup type /stringtype eq { pop } if } if newpath } def /u { } def /U { } def /q { _pola 0 eq { gsave } if } def /Q { _pola 0 eq { grestore } if } def /*u { _pola 1 add /_pola exch ddef } def /*U { _pola 1 sub /_pola exch ddef _pola 0 eq { CRender } if } def /D { pop } def /*w { } def /*W { } def /` { /_i save ddef clipForward? { nulldevice } if 6 1 roll 4 npop concat pop userdict begin /showpage { } def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash /setstrokeadjust where {pop false setstrokeadjust} if newpath 0 setgray false setoverprint } def /~ { end _i restore } def /_rgbtocmyk { 3 { 1 exch sub 3 1 roll } repeat 3 copy 1 4 1 roll 3 { 3 index 2 copy gt { exch } if pop 4 1 roll } repeat pop pop pop 4 1 roll 3 { 3 index sub 3 1 roll } repeat 4 -1 roll } def /setrgbfill { _rgbf astore pop /_fc { _lp /fill ne { _of setoverprint _rgbf aload pop setrgbcolor /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc hvashow } ddef /_pjsf { _fc hvawidthshow } ddef /_lp /none ddef } def /setrgbstroke { _rgbs astore pop /_sc { _lp /stroke ne { _os setoverprint _rgbs aload pop setrgbcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /O { 0 ne /_of exch ddef /_lp /none ddef } def /R { 0 ne /_os exch ddef /_lp /none ddef } def /g { /_gf exch ddef /_fc { _lp /fill ne { _of setoverprint _gf setgray /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc hvashow } ddef /_pjsf { _fc hvawidthshow } ddef /_lp /none ddef } def /G { /_gs exch ddef /_sc { _lp /stroke ne { _os setoverprint _gs setgray /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /k { _cf astore pop /_fc { _lp /fill ne { _of setoverprint _cf aload pop setcmykcolor /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc hvashow } ddef /_pjsf { _fc hvawidthshow } ddef /_lp /none ddef } def /K { _cs astore pop /_sc { _lp /stroke ne { _os setoverprint _cs aload pop setcmykcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /Xa { _?cmyk { 3 npop k }{ setrgbfill 4 npop } ifelse } def /XA { _?cmyk { 3 npop K }{ setrgbstroke 4 npop } ifelse } def /Xs { /_gf exch ddef 5 npop /_fc { _lp /fill ne { _of setoverprint _gf setAIseparationgray /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc hvashow } ddef /_pjsf { _fc hvawidthshow } ddef /_lp /none ddef } def /XS { /_gs exch ddef 5 npop /_sc { _lp /stroke ne { _os setoverprint _gs setAIseparationgray /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /Xx { exch /_gf exch ddef 0 eq { findcmykcustomcolor }{ _?cmyk {true}{/findrgbcustomcolor where{pop false}{true}ifelse}ifelse { 4 1 roll 3 npop findcmykcustomcolor }{ 8 -4 roll 4 npop findrgbcustomcolor } ifelse } ifelse /_if exch ddef /_fc { _lp /fill ne { _of setoverprint _if _gf 1 exch sub setcustomcolor /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc hvashow } ddef /_pjsf { _fc hvawidthshow } ddef /_lp /none ddef } def /XX { exch /_gs exch ddef 0 eq { findcmykcustomcolor }{ _?cmyk {true}{/findrgbcustomcolor where{pop false}{true}ifelse}ifelse { 4 1 roll 3 npop findcmykcustomcolor }{ 8 -4 roll 4 npop findrgbcustomcolor } ifelse } ifelse /_is exch ddef /_sc { _lp /stroke ne { _os setoverprint _is _gs 1 exch sub setcustomcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /x { /_gf exch ddef findcmykcustomcolor /_if exch ddef /_fc { _lp /fill ne { _of setoverprint _if _gf 1 exch sub setcustomcolor /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc hvashow } ddef /_pjsf { _fc hvawidthshow } ddef /_lp /none ddef } def /X { /_gs exch ddef findcmykcustomcolor /_is exch ddef /_sc { _lp /stroke ne { _os setoverprint _is _gs 1 exch sub setcustomcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /XK { 3 -1 roll pop 0 eq { 1 exch sub 3 {dup 3 1 roll mul 5 1 roll} repeat mul 4 1 roll K } { 1 exch sub 4 1 roll 3 {1 exch sub 3 index mul 1 exch sub 3 1 roll} repeat 4 -1 roll pop XA } ifelse } def /Xk { 3 -1 roll pop 0 eq { 1 exch sub 3 {dup 3 1 roll mul 5 1 roll} repeat mul 4 1 roll k } { 1 exch sub 4 1 roll 3 {1 exch sub 3 index mul 1 exch sub 3 1 roll} repeat 4 -1 roll pop Xa } ifelse } def /A { pop } def /annotatepage { userdict /annotatepage 2 copy known {get exec} {pop pop} ifelse } def /XT { pop pop } def /Xt { pop } def /discard { save /discardSave exch store discardDict begin /endString exch store gt38? { 2 add } if load stopped pop end discardSave restore } bind def userdict /discardDict 7 dict dup begin put /pre38Initialize { /endStringLength endString length store /newBuff buffer 0 endStringLength getinterval store /newBuffButFirst newBuff 1 endStringLength 1 sub getinterval store /newBuffLast newBuff endStringLength 1 sub 1 getinterval store } def /shiftBuffer { newBuff 0 newBuffButFirst putinterval newBuffLast 0 currentfile read not { stop } if put } def 0 { pre38Initialize mark currentfile newBuff readstring exch pop { { newBuff endString eq { cleartomark stop } if shiftBuffer } loop } { stop } ifelse } def 1 { pre38Initialize /beginString exch store mark currentfile newBuff readstring exch pop { { newBuff beginString eq { /layerCount dup load 1 add store } { newBuff endString eq { /layerCount dup load 1 sub store layerCount 0 eq { cleartomark stop } if } if } ifelse shiftBuffer } loop } if } def 2 { mark { currentfile buffer {readline} stopped { % assume error was due to overfilling the buffer }{ not { stop } if endString eq { cleartomark stop } if }ifelse } loop } def 3 { /beginString exch store /layerCnt 1 store mark { currentfile buffer {readline} stopped { % assume error was due to overfilling the buffer }{ not { stop } if dup beginString eq { pop /layerCnt dup load 1 add store } { endString eq { layerCnt 1 eq { cleartomark stop } { /layerCnt dup load 1 sub store } ifelse } if } ifelse }ifelse } loop } def end userdict /clipRenderOff 15 dict dup begin put { /n /N /s /S /f /F /b /B } { { _doClip 1 eq { /_doClip 0 ddef _eo {eoclip} {clip} ifelse } if newpath } def } forall /Tr /pop load def /Bb {} def /BB /pop load def /Bg {12 npop} def /Bm {6 npop} def /Bc /Bm load def /Bh {4 npop} def end /Lb { 6 npop 7 2 roll 5 npop 0 eq { 0 eq { (%AI5_BeginLayer) 1 (%AI5_EndLayer--) discard } { /clipForward? true def /Tx /pop load def /Tj /pop load def currentdict end clipRenderOff begin begin } ifelse } { 0 eq { save /discardSave exch store } if } ifelse } bind def /LB { discardSave dup null ne { restore } { pop clipForward? { currentdict end end begin /clipForward? false ddef } if } ifelse } bind def /Pb { pop pop 0 (%AI5_EndPalette) discard } bind def /Np { 0 (%AI5_End_NonPrinting--) discard } bind def /Ln /pop load def /Ap /pop load def /Ar { 72 exch div 0 dtransform dup mul exch dup mul add sqrt dup 1 lt { pop 1 } if setflat } def /Mb { q } def /Md { } def /MB { Q } def /nc 4 dict def nc begin /setgray { pop } bind def /setcmykcolor { 4 npop } bind def /setrgbcolor { 3 npop } bind def /setcustomcolor { 2 npop } bind def currentdict readonly pop end /XP { 4 npop } bind def /XD { pop } bind def end setpacking %%EndResource %%BeginResource: procset Adobe_cshow 2.0 8 %%Title: (Writing System Operators) %%Version: 2.0 8 %%CreationDate: (1/23/89) () %%Copyright: ((C) 1992-1996 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_cshow 14 dict dup begin put /initialize { Adobe_cshow begin Adobe_cshow { dup xcheck { bind } if pop pop } forall end Adobe_cshow begin } def /terminate { currentdict Adobe_cshow eq { end } if } def /cforall { /_lobyte 0 ddef /_hibyte 0 ddef /_cproc exch ddef /_cscript currentfont /FontScript known { currentfont /FontScript get } { -1 } ifelse ddef { /_lobyte exch ddef _hibyte 0 eq _cscript 1 eq _lobyte 129 ge _lobyte 159 le and _lobyte 224 ge _lobyte 252 le and or and _cscript 2 eq _lobyte 161 ge _lobyte 254 le and and _cscript 3 eq _lobyte 161 ge _lobyte 254 le and and _cscript 25 eq _lobyte 161 ge _lobyte 254 le and and _cscript -1 eq or or or or and { /_hibyte _lobyte ddef } { _hibyte 256 mul _lobyte add _cproc /_hibyte 0 ddef } ifelse } forall } def /cstring { dup 256 lt { (s) dup 0 4 3 roll put } { dup 256 idiv exch 256 mod (hl) dup dup 0 6 5 roll put 1 4 3 roll put } ifelse } def /clength { 0 exch { 256 lt { 1 } { 2 } ifelse add } cforall } def /hawidthshow { { dup cstring show _hvax _hvay rmoveto _hvwb eq { _hvcx _hvcy rmoveto } if } cforall } def /vawidthshow { { dup 255 le _charorientation 1 eq and { -90 rotate 0 _fontRotateAdjust rmoveto cstring _hvcx _hvcy _hvwb _hvax _hvay 6 -1 roll awidthshow 0 _fontRotateAdjust neg rmoveto 90 rotate } { currentpoint _fontHeight sub exch _hvay sub exch _hvax sub 2 index _hvwb eq { exch _hvcy sub exch _hvcx sub } if 3 2 roll cstring dup stringwidth pop 2 div neg _fontAscent neg rmoveto show moveto } ifelse } cforall } def /hvawidthshow { 6 1 roll /_hvay exch ddef /_hvax exch ddef /_hvwb exch ddef /_hvcy exch ddef /_hvcx exch ddef _lineorientation 0 eq { hawidthshow } { vawidthshow } ifelse } def /hvwidthshow { 0 0 3 -1 roll hvawidthshow } def /hvashow { 0 0 0 6 -3 roll hvawidthshow } def /hvshow { 0 0 0 0 0 6 -1 roll hvawidthshow } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_shading_AI8 1.0 0 %%Title: (Adobe Illustrator 8 Shading Procset) %%Version: 1.0 0 %%CreationDate: (12/17/97) () %%Copyright: ((C) 1987-1997 Adobe Systems Incorporated All Rights Reserved) userdict /defaultpacking currentpacking put true setpacking userdict /Adobe_shading_AI8 10 dict dup begin put /initialize { Adobe_shading_AI8 begin Adobe_shading_AI8 bdprocs Mesh /initialize get exec } def /terminate { currentdict Adobe_shading_AI8 eq { end } if } def /bdprocs { { dup xcheck 1 index type /arraytype eq and { bind } if pop pop } forall } def /X! {pop} def /X# {pop pop} def /Mesh 40 dict def Mesh begin /initialize { Mesh bdprocs Mesh begin /emulate? /AI8MeshEmulation where { pop AI8MeshEmulation }{ systemdict /shfill known not } ifelse def end } def /bd { shadingdict begin } def /paint { emulate? { end }{ /_lp /none ddef _fc /_lp /none ddef /AIColorSpace AIColorSpace tocolorspace store /ColorSpace AIColorSpace topsspace store version_ge_3010.106 not systemdict /setsmoothness known and { 0.0001 setsmoothness } if composite? { /DataSource getdatasrc def Matrix concat currentdict end shfill }{ AIColorSpace makesmarks AIPlateList markingplate and not isoverprint and { end }{ /ColorSpace /DeviceGray store /Decode [0 1 0 1 0 1] store /DataSource getplatesrc def Matrix concat currentdict end shfill } ifelse } ifelse } ifelse } def /shadingdict 12 dict def shadingdict begin /ShadingType 6 def /BitsPerCoordinate 16 def /BitsPerComponent 8 def /BitsPerFlag 8 def end /datafile null def /databuf 256 string def /dataptr 0 def /srcspace null def /srcchannels 0 def /dstchannels 0 def /dstplate 0 def /srctodstcolor null def /getplatesrc { /srcspace AIColorSpace store /srcchannels AIColorSpace getnchannels store /dstchannels 1 store /dstplate getplateindex store /srctodstcolor srcspace makesmarks { dstplate 4 eq { {1 exch sub} }{ {srcspace tocmyk 3 dstplate sub index 1 exch sub 5 1 roll 4 {pop} repeat} } ifelse }{ {srcchannels {pop} repeat 1} } ifelse store /datafile getdatasrc store /rdpatch168 load DataLength () /SubFileDecode filter } def /getdatasrc { /rdcmntline load /ASCII85Decode filter } def /rdpatch168 { /dataptr 0 store 49 rdcount 4 { dup {pop srcchannels getint8} if dup {pop srctodstcolor dstchannels putint8 true} if } repeat {databuf 0 dataptr getinterval}{()} ifelse } def /rdpatch3216 { /dataptr 0 store 97 rdcount 4 { dup {pop srcchannels getint16} if dup {pop srctodstcolor dstchannels putint16 true} if } repeat {databuf 0 dataptr getinterval}{()} ifelse } def /rdcount { dup 0 gt { datafile databuf dataptr 4 -1 roll getinterval readstring exch length dataptr add /dataptr exch store }{ true } ifelse } def /getint8 { mark true 3 -1 roll { dup {pop datafile read} if dup {pop 255 div true} if } repeat { counttomark 1 add -1 roll pop true }{ cleartomark false } ifelse } def /putint8 { dup dataptr add /dataptr exch store dataptr exch { 1 sub exch 255 mul cvi databuf 2 index 3 -1 roll put } repeat pop } def /getint16 { mark true 3 -1 roll { dup {pop datafile read} if dup {pop 256 mul datafile read} if dup {pop add 65535 div true} if } repeat { counttomark 1 add -1 roll pop true }{ cleartomark false } ifelse } def /putint16 { dup 2 mul dataptr add /dataptr exch store dataptr exch { 2 sub exch 65535 mul cvi dup 256 idiv databuf 3 index 3 -1 roll put 256 mod databuf 2 index 1 add 3 -1 roll put } repeat pop } def /srcbuf 256 string def /rdcmntline { currentfile srcbuf readline pop (%) anchorsearch {pop} if } def /getplateindex { 0 [cyan? magenta? yellow? black? customColor?] {{exit} if 1 add} forall } def /aicsarray 4 array def /aicsaltvals 4 array def /aicsaltcolr aicsaltvals def /tocolorspace { dup type /arraytype eq { mark exch aload pop aicsarray 0 3 -1 roll put aicsarray 1 3 -1 roll put dup aicsarray 2 3 -1 roll put gettintxform aicsarray 3 3 -1 roll put counttomark aicsaltvals 0 3 -1 roll getinterval /aicsaltcolr exch store aicsaltcolr astore pop pop aicsarray } if } def /subtintxform {aicsaltcolr {1 index mul exch} forall pop} def /addtintxform {aicsaltcolr {1 sub 1 index mul 1 add exch} forall pop} def /gettintxform { /DeviceRGB eq {/addtintxform}{/subtintxform} ifelse load } def /getnchannels { dup type /arraytype eq {0 get} if colorspacedict exch get begin Channels end } def /makesmarks { composite? { pop true }{ dup dup type /arraytype eq {0 get} if colorspacedict exch get begin MarksPlate end } ifelse } def /markingplate { composite? { pop true }{ dup type /arraytype eq { dup length getplateindex gt {getplateindex get}{pop false} ifelse } if } ifelse } def /tocmyk { dup dup type /arraytype eq {0 get} if colorspacedict exch get begin ToCMYK end } def /topsspace { dup dup type /arraytype eq {0 get} if colorspacedict exch get begin ToPSSpace end } def /colorspacedict 5 dict dup begin /DeviceGray 4 dict dup begin /Channels 1 def /MarksPlate {pop black?} def /ToCMYK {pop 1 exch sub 0 0 0 4 -1 roll} def /ToPSSpace {} def end def /DeviceRGB 4 dict dup begin /Channels 3 def /MarksPlate {pop isCMYKSep?} def /ToCMYK {pop _rgbtocmyk} def /ToPSSpace {} def end def /DeviceCMYK 4 dict dup begin /Channels 4 def /MarksPlate {pop isCMYKSep?} def /ToCMYK {pop} def /ToPSSpace {} def end def /Separation 4 dict dup begin /Channels 1 def /MarksPlate { /findcmykcustomcolor where { pop dup 1 exch ToCMYK 5 -1 roll 1 get findcmykcustomcolor 1 setcustomcolor systemdict /currentgray get exec 1 ne }{ pop false } ifelse } def /ToCMYK { dup 2 get mark exch 4 2 roll 3 get exec counttomark -1 roll tocmyk 5 -1 roll pop } def /ToPSSpace {} def end def /Process 4 dict dup begin /Channels 1 def /MarksPlate { isCMYKSep? { 1 exch ToCMYK 4 array astore getplateindex get 0 ne }{ pop false } ifelse } def /ToCMYK { dup 2 get mark exch 4 2 roll 3 get exec counttomark -1 roll tocmyk 5 -1 roll pop } def /ToPSSpace { 4 array copy dup 0 /Separation put } def end def end def /isoverprint { /currentoverprint where {pop currentoverprint}{_of} ifelse } def /version_ge_3010.106 { version {cvr} stopped { pop false }{ 3010.106 ge } ifelse } def end end defaultpacking setpacking %%EndResource %%EndProlog %%BeginSetup userdict /_useSmoothShade false put userdict /_aicmykps true put userdict /_forceToCMYK true put Adobe_level2_AI5 /initialize get exec Adobe_cshow /initialize get exec Adobe_Illustrator_AI5_vars Adobe_Illustrator_AI5 Adobe_typography_AI5 /initialize get exec Adobe_ColorImage_AI6 /initialize get exec Adobe_shading_AI8 /initialize get exec Adobe_Illustrator_AI5 /initialize get exec %AI3_BeginRider currentpacking true setpacking %%BeginFont: Symbol %!PS-AdobeFont-1.0: Symbol 001.008 %%CreationDate: Fri Mar 28 22:03:48 1997 %%VMusage: 30820 39997 11 dict begin /FontInfo 10 dict dup begin /version (001.008) readonly def /Notice (Copyright (c) 1985, 1987, 1989, 1990, 1997 Adobe Systems Incorporated. All rights reserved.) readonly def /FullName (Symbol) readonly def /FamilyName (Symbol) readonly def /Weight (Medium) readonly def /isFixedPitch false def /ItalicAngle 0 def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /Symbol def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 32 /space put dup 33 /exclam put dup 34 /universal put dup 35 /numbersign put dup 36 /existential put dup 37 /percent put dup 38 /ampersand put dup 39 /suchthat put dup 40 /parenleft put dup 41 /parenright put dup 42 /asteriskmath put dup 43 /plus put dup 44 /comma put dup 45 /minus put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 60 /less put dup 61 /equal put dup 62 /greater put dup 63 /question put dup 64 /congruent put dup 65 /Alpha put dup 66 /Beta put dup 67 /Chi put dup 68 /Delta put dup 69 /Epsilon put dup 70 /Phi put dup 71 /Gamma put dup 72 /Eta put dup 73 /Iota put dup 74 /theta1 put dup 75 /Kappa put dup 76 /Lambda put dup 77 /Mu put dup 78 /Nu put dup 79 /Omicron put dup 80 /Pi put dup 81 /Theta put dup 82 /Rho put dup 83 /Sigma put dup 84 /Tau put dup 85 /Upsilon put dup 86 /sigma1 put dup 87 /Omega put dup 88 /Xi put dup 89 /Psi put dup 90 /Zeta put dup 91 /bracketleft put dup 92 /therefore put dup 93 /bracketright put dup 94 /perpendicular put dup 95 /underscore put dup 96 /radicalex put dup 97 /alpha put dup 98 /beta put dup 99 /chi put dup 100 /delta put dup 101 /epsilon put dup 102 /phi put dup 103 /gamma put dup 104 /eta put dup 105 /iota put dup 106 /phi1 put dup 107 /kappa put dup 108 /lambda put dup 109 /mu put dup 110 /nu put dup 111 /omicron put dup 112 /pi put dup 113 /theta put dup 114 /rho put dup 115 /sigma put dup 116 /tau put dup 117 /upsilon put dup 118 /omega1 put dup 119 /omega put dup 120 /xi put dup 121 /psi put dup 122 /zeta put dup 123 /braceleft put dup 124 /bar put dup 125 /braceright put dup 126 /similar put dup 160 /Euro put dup 161 /Upsilon1 put dup 162 /minute put dup 163 /lessequal put dup 164 /fraction put dup 165 /infinity put dup 166 /florin put dup 167 /club put dup 168 /diamond put dup 169 /heart put dup 170 /spade put dup 171 /arrowboth put dup 172 /arrowleft put dup 173 /arrowup put dup 174 /arrowright put dup 175 /arrowdown put dup 176 /degree put dup 177 /plusminus put dup 178 /second put dup 179 /greaterequal put dup 180 /multiply put dup 181 /proportional put dup 182 /partialdiff put dup 183 /bullet put dup 184 /divide put dup 185 /notequal put dup 186 /equivalence put dup 187 /approxequal put dup 188 /ellipsis put dup 189 /arrowvertex put dup 190 /arrowhorizex put dup 191 /carriagereturn put dup 192 /aleph put dup 193 /Ifraktur put dup 194 /Rfraktur put dup 195 /weierstrass put dup 196 /circlemultiply put dup 197 /circleplus put dup 198 /emptyset put dup 199 /intersection put dup 200 /union put dup 201 /propersuperset put dup 202 /reflexsuperset put dup 203 /notsubset put dup 204 /propersubset put dup 205 /reflexsubset put dup 206 /element put dup 207 /notelement put dup 208 /angle put dup 209 /gradient put dup 210 /registerserif put dup 211 /copyrightserif put dup 212 /trademarkserif put dup 213 /product put dup 214 /radical put dup 215 /dotmath put dup 216 /logicalnot put dup 217 /logicaland put dup 218 /logicalor put dup 219 /arrowdblboth put dup 220 /arrowdblleft put dup 221 /arrowdblup put dup 222 /arrowdblright put dup 223 /arrowdbldown put dup 224 /lozenge put dup 225 /angleleft put dup 226 /registersans put dup 227 /copyrightsans put dup 228 /trademarksans put dup 229 /summation put dup 230 /parenlefttp put dup 231 /parenleftex put dup 232 /parenleftbt put dup 233 /bracketlefttp put dup 234 /bracketleftex put dup 235 /bracketleftbt put dup 236 /bracelefttp put dup 237 /braceleftmid put dup 238 /braceleftbt put dup 239 /braceex put dup 241 /angleright put dup 242 /integral put dup 243 /integraltp put dup 244 /integralex put dup 245 /integralbt put dup 246 /parenrighttp put dup 247 /parenrightex put dup 248 /parenrightbt put dup 249 /bracketrighttp put dup 250 /bracketrightex put dup 251 /bracketrightbt put dup 252 /bracerighttp put dup 253 /bracerightmid put dup 254 /bracerightbt put readonly def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] def /UniqueID 42996 def /FontBBox{-180 -293 1090 1010}readonly def currentdict end currentfile eexec 8dda0385bbe2e28975521ce366a1efbcd19951c755b299f7de57699ffa32088176bbcfeb9d3d075a656fc2d3ffadac652e0956194030c65b6ac7dfb4cce0096cf30964c72ac7742ef0dfd71d6aeda00d45b6c86f2ebeadafcc658a64b076f436a780849440223f266d2dab36e19a62bf7550db533ad06fe9bb6bb7ebaf6f78 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: Times-Roman %!PS-AdobeFont-1.0: Times-Roman 002.000 %%CreationDate: Thu May 1 14:12:30 1997 %%VMusage: 34396 41288 %% The digitally encoded machine readable software for producing the %% Typefaces licensed to you is copyrighted (c) 1985, 1987, 1989, 1990, 1993, %% 1997 Adobe Systems. All Rights Reserved. This software is the property of %% Adobe Systems Incorporated and its licensors, and may not be reproduced, %% used, displayed, modified, disclosed or transferred without the express %% written approval of Adobe. The digitally encoded machine readable %% outline data for producing the Typefaces licensed to you is copyrighted (c) %% 1981, 1997 Linotype-Hell AG and/or its subsidiaries. All Rights Reserved. %% This data is the property of Linotype-Hell AG and/or its subsidiaries and %% may not be reproduced, used, displayed, modified, disclosed or transferred %% without the express written approval of Linotype-Hell AG and/or its %% subsidiaries. %% Times is a trademark of Linotype-Hell AG and/or its subsidiaries. 11 dict begin /FontInfo 10 dict dup begin /version (002.000) readonly def /Notice (Copyright (c) 1985, 1987, 1989, 1990, 1993, 1997 Adobe Systems Incorporated. All Rights Reserved.Times is a trademark of Linotype-Hell AG and/or its subsidiaries.) readonly def /Copyright ( The digitally encoded machine readable software for producing the Typefaces licensed to you is copyrighted (c) 1985, 1987, 1989, 1990, 1993, 1997 Adobe Systems. All Rights Reserved. This software is the property of Adobe Systems Incorporated and its licensors, and may not be reproduced, used, displayed, modified, disclosed or transferred without the express written approval of Adobe. The digitally encoded machine readable outline data for producing the Typefaces licensed to you is copyrighted (c) 1981, 1997 Linotype-Hell AG and/or its subsidiaries. All Rights Reserved. This data is the property of Linotype-Hell AG and/or its subsidiaries and may not be reproduced, used, displayed, modified, disclosed or transferred without the express written approval of Linotype-Hell AG and/or its subsidiaries. ) readonly def /FullName (Times Roman) readonly def /FamilyName (Times) readonly def /Weight (Roman) readonly def /isFixedPitch false def /ItalicAngle 0 def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /Times-Roman def /Encoding StandardEncoding def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] def /UniqueID 43146 def /FontBBox{-168 -218 1000 898}readonly def currentdict end currentfile eexec 8b6e5d94c2011e84337eb6aa8c9f94ed23d9d874b2b6213329d8b14e7506c2c44191fca634722de2d7517eddbf38a72143aa3731f22db880be1deb8d8c4b788fb50b26512e484404a443792a51c31c744b2a234a2aa147e9d791b3080b004f961e6185a1d88823c51ef3cb1e5efc14bc413a0f87a484401ff1de26e0403ac6 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780.7417 c S 0.25 w [2 ]0 d 180.4541 729.5811 m 180.4541 739.4126 184.7939 753.4351 194.7998 765.6646 c 201.1519 773.4282 208.5625 779.2402 215.4868 783.6138 c S 0 To 0.7071 0.7071 -0.7071 0.7071 188.9702 764.3657 0 Tp 0 Tv TP 0 Tr 0 O 0 0 0 1 k 1 w []0 d /_Times-Roman 9 8.082 -1.9619 Tf (Hopf) Tx 1 0 Tk (\r) TX TO /BBAccumRotation (0.785397) XT 0 To 0.7071 0.7071 -0.7071 0.7071 188.2671 735.4106 0 Tp 0 Tv TP 0 Tr (homoclinic) Tx 1 0 Tk (\r) TX TO /BBAccumRotation (0.785397) XT LB %AI5_EndLayer-- %%PageTrailer gsave annotatepage grestore showpage %%Trailer Adobe_Illustrator_AI5 /terminate get exec Adobe_shading_AI8 /terminate get exec Adobe_ColorImage_AI6 /terminate get exec Adobe_typography_AI5 /terminate get exec Adobe_cshow /terminate get exec Adobe_level2_AI5 /terminate get exec %%EOF EndOfTheIncludedPostscriptMagicCookie % Here is the PostScript for gelfreich_fig_2.eps: \message{Writing file gelfreich_fig_2.eps} \psdump{gelfreich_fig_2.eps} %!PS-Adobe-3.0 EPSF-3.0 %%Creator: Adobe Illustrator(R) 8.0 %%AI8_CreatorVersion: 8 %%For: (x y) (FU-Berlin) %%Title: (gelfreich_fig_2.eps) %%CreationDate: (1/2/02) (5:42 PM) %%BoundingBox: 107 633 438 730 %%HiResBoundingBox: 107.2632 633.1362 437.8525 729.9854 %%DocumentProcessColors: Black %%DocumentFonts: Times-Italic %%DocumentNeededFonts: Times-Italic %%DocumentSuppliedResources: procset Adobe_level2_AI5 1.2 0 %%+ procset Adobe_typography_AI5 1.0 1 %%+ procset Adobe_ColorImage_AI6 1.3 0 %%+ procset Adobe_Illustrator_AI5 1.3 0 %%+ procset Adobe_cshow 2.0 8 %%+ procset Adobe_shading_AI8 1.0 0 %AI5_FileFormat 4.0 %AI3_ColorUsage: Black&White %AI3_IncludePlacedImages %AI7_ImageSettings: 1 %%CMYKProcessColor: 1 1 1 1 ([Passermarken]) %%AI6_ColorSeparationSet: 1 1 (AI6 Default Color Separation Set) %%+ Options: 1 16 0 1 0 1 1 1 0 1 1 1 1 8.504 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 2 3 4 %%+ PPD: 1 21 0 0 60 45 2 2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 () %AI3_TemplateBox: 297.5 420.5 297.5 420.5 %AI3_TileBox: 14 13 581 830 %AI3_DocumentPreview: Header %AI5_ArtSize: 595 842 %AI5_RulerUnits: 2 %AI5_ArtFlags: 1 0 0 1 0 0 1 0 0 %AI5_TargetResolution: 800 %AI5_NumLayers: 1 %AI8_OpenToView: 169.7163 721.7349 6.78 953 693 18 0 1 11 68 0 0 %AI5_OpenViewLayers: 7 %%PageOrigin:14 13 %%AI3_PaperRect:-14 830 581 -12 %%AI3_Margin:14 -13 -14 12 %AI7_GridSettings: 72 8 72 8 1 0 0.8 0.8 0.8 0.9 0.9 0.9 %%EndComments %%BeginProlog %%BeginResource: procset Adobe_level2_AI5 1.2 0 %%Title: (Adobe Illustrator (R) Version 5.0 Level 2 Emulation) %%Version: 1.2 0 %%CreationDate: (04/10/93) () %%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved) userdict /Adobe_level2_AI5 26 dict dup begin put /packedarray where not { userdict begin /packedarray { array astore readonly } bind def /setpacking /pop load def /currentpacking false def end 0 } if pop userdict /defaultpacking currentpacking put true setpacking /initialize { Adobe_level2_AI5 begin } bind def /terminate { currentdict Adobe_level2_AI5 eq { end } if } bind def mark /setcustomcolor where not { /findcmykcustomcolor { (AI8_CMYK_CustomColor) 6 packedarray } bind def /findrgbcustomcolor { (AI8_RGB_CustomColor) 5 packedarray } bind def /setcustomcolor { exch aload pop dup (AI8_CMYK_CustomColor) eq { pop pop 4 { 4 index mul 4 1 roll } repeat 5 -1 roll pop setcmykcolor } { dup (AI8_RGB_CustomColor) eq { pop pop 3 { 1 exch sub 3 index mul 1 exch sub 3 1 roll } repeat 4 -1 roll pop setrgbcolor } { pop 4 { 4 index mul 4 1 roll } repeat 5 -1 roll pop setcmykcolor } ifelse } ifelse } def } if /setAIseparationgray { false setoverprint 0 setgray /setseparationgray where{ pop setseparationgray }{ /setcolorspace where{ pop [/Separation (All) /DeviceCMYK {dup dup dup}] setcolorspace 1 exch sub setcolor }{ setgray }ifelse }ifelse } def /gt38? mark {version cvr cvx exec} stopped {cleartomark true} {38 gt exch pop} ifelse def userdict /deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt put userdict /level2? systemdict /languagelevel known dup { pop systemdict /languagelevel get 2 ge } if put /level2ScreenFreq { begin 60 HalftoneType 1 eq { pop Frequency } if HalftoneType 2 eq { pop GrayFrequency } if HalftoneType 5 eq { pop Default level2ScreenFreq } if end } bind def userdict /currentScreenFreq level2? {currenthalftone level2ScreenFreq} {currentscreen pop pop} ifelse put level2? not { /setcmykcolor where not { /setcmykcolor { exch .11 mul add exch .59 mul add exch .3 mul add 1 exch sub setgray } def } if /currentcmykcolor where not { /currentcmykcolor { 0 0 0 1 currentgray sub } def } if /setoverprint where not { /setoverprint /pop load def } if /selectfont where not { /selectfont { exch findfont exch dup type /arraytype eq { makefont } { scalefont } ifelse setfont } bind def } if /cshow where not { /cshow { [ 0 0 5 -1 roll aload pop ] cvx bind forall } bind def } if } if cleartomark /anyColor? { add add add 0 ne } bind def /testColor { gsave setcmykcolor currentcmykcolor grestore } bind def /testCMYKColorThrough { testColor anyColor? } bind def userdict /composite? 1 0 0 0 testCMYKColorThrough 0 1 0 0 testCMYKColorThrough 0 0 1 0 testCMYKColorThrough 0 0 0 1 testCMYKColorThrough and and and put composite? not { userdict begin gsave /cyan? 1 0 0 0 testCMYKColorThrough def /magenta? 0 1 0 0 testCMYKColorThrough def /yellow? 0 0 1 0 testCMYKColorThrough def /black? 0 0 0 1 testCMYKColorThrough def grestore /isCMYKSep? cyan? magenta? yellow? black? or or or def /customColor? isCMYKSep? not def end } if end defaultpacking setpacking %%EndResource %%BeginResource: procset Adobe_typography_AI5 1.0 1 %%Title: (Typography Operators) %%Version: 1.0 1 %%CreationDate:(6/10/1996) () %%Copyright: ((C) 1987-1996 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_typography_AI5 68 dict dup begin put /initialize { begin begin Adobe_typography_AI5 begin Adobe_typography_AI5 { dup xcheck { bind } if pop pop } forall end end end Adobe_typography_AI5 begin } def /terminate { currentdict Adobe_typography_AI5 eq { end } if } def /modifyEncoding { /_tempEncode exch ddef /_pntr 0 ddef { counttomark -1 roll dup type dup /marktype eq { pop pop exit } { /nametype eq { _tempEncode /_pntr dup load dup 3 1 roll 1 add ddef 3 -1 roll put } { /_pntr exch ddef } ifelse } ifelse } loop _tempEncode } def /havefont { systemdict /languagelevel known { /Font resourcestatus dup { exch pop exch pop } if } { systemdict /FontDirectory get 1 index known { pop true } { systemdict /fileposition known { dup length 6 add exch Ss 6 250 getinterval cvs pop Ss exch 0 exch getinterval status { pop pop pop pop true } { false } ifelse } { pop false } ifelse } ifelse } ifelse } def /TE { StandardEncoding 256 array copy modifyEncoding /_nativeEncoding exch def } def /subststring { exch 2 index exch search { exch pop exch dup () eq { pop exch concatstring } { 3 -1 roll exch concatstring concatstring } ifelse exch pop true } { pop pop false } ifelse } def /concatstring { 1 index length 1 index length 1 index add string dup 0 5 index putinterval dup 2 index 4 index putinterval 4 1 roll pop pop pop } def % /TZ { dup type /arraytype eq { /_wv exch def } { /_wv 0 def } ifelse /_useNativeEncoding exch def 2 index havefont { 3 index 255 string cvs dup (_Symbol_) eq { pop 2 index findfont } { 1 index 0 eq { dup length 1 sub 1 exch getinterval cvn findfont } { pop 2 index findfont } ifelse } ifelse } { dup 1 eq { 2 index 64 string cvs dup (-90pv-RKSJ-) (-83pv-RKSJ-) subststring { exch pop dup havefont { findfont false } { pop true } ifelse } { pop dup (-90ms-RKSJ-) (-Ext-RKSJ-) subststring { exch pop dup havefont { findfont false } { pop true } ifelse } { pop pop true } ifelse } ifelse { 1 index 1 eq { /Ryumin-Light-Ext-RKSJ-V havefont {/Ryumin-Light-Ext-RKSJ-V} {/Courier} ifelse } { /Ryumin-Light-83pv-RKSJ-H havefont {/Ryumin-Light-83pv-RKSJ-H} {/Courier} ifelse } ifelse findfont [1 0 0.5 1 0 0] makefont } if } { /Courier findfont } ifelse } ifelse _wv type /arraytype eq { _wv makeblendedfont } if dup length 10 add dict begin mark exch { 1 index /FID ne { def } if cleartomark mark } forall pop /FontScript exch def /FontDirection exch def /FontRequest exch def /FontName exch def counttomark 0 eq { 1 _useNativeEncoding eq { /Encoding _nativeEncoding def } if cleartomark } { /Encoding load 256 array copy modifyEncoding /Encoding exch def } ifelse FontName currentdict end definefont pop } def /tr { _ax _ay 3 2 roll } def /trj { _cx _cy _sp _ax _ay 6 5 roll } def /a0 { /Tx { dup currentpoint 3 2 roll tr _psf newpath moveto tr _ctm _pss } ddef /Tj { dup currentpoint 3 2 roll trj _pjsf newpath moveto trj _ctm _pjss } ddef } def /a1 { W B } def /e0 { /Tx { tr _psf } ddef /Tj { trj _pjsf } ddef } def /e1 { W F } def /i0 { /Tx { tr sp } ddef /Tj { trj jsp } ddef } def /i1 { W N } def /o0 { /Tx { tr sw rmoveto } ddef /Tj { trj swj rmoveto } ddef } def /r0 { /Tx { tr _ctm _pss } ddef /Tj { trj _ctm _pjss } ddef } def /r1 { W S } def /To { pop _ctm currentmatrix pop } def /TO { iTe _ctm setmatrix newpath } def /Tp { pop _tm astore pop _ctm setmatrix _tDict begin /W { } def /h { } def } def /TP { end iTm 0 0 moveto } def /Tr { _render 3 le { currentpoint newpath moveto } if dup 8 eq { pop 0 } { dup 9 eq { pop 1 } if } ifelse dup /_render exch ddef _renderStart exch get load exec } def /iTm { _ctm setmatrix _tm concat _shift aload pop _lineorientation 1 eq { exch } if translate _scale aload pop _lineorientation 1 eq _yokoorientation 1 eq or { exch } if scale } def /Tm { _tm astore pop iTm 0 0 moveto } def /Td { _mtx translate _tm _tm concatmatrix pop iTm 0 0 moveto } def /iTe { _render -1 eq { } { _renderEnd _render get dup null ne { load exec } { pop } ifelse } ifelse /_render -1 ddef } def /Ta { pop } def /Tf { 1 index type /nametype eq { dup 0.75 mul 1 index 0.25 mul neg } if /_fontDescent exch ddef /_fontAscent exch ddef /_fontSize exch ddef /_fontRotateAdjust _fontAscent _fontDescent add 2 div neg ddef /_fontHeight _fontSize ddef findfont _fontSize scalefont setfont } def /Tl { pop neg 0 exch _leading astore pop } def /Tt { pop } def /TW { 3 npop } def /Tw { /_cx exch ddef } def /TC { 3 npop } def /Tc { /_ax exch ddef } def /Ts { 0 exch _shift astore pop currentpoint iTm moveto } def /Ti { 3 npop } def /Tz { count 1 eq { 100 } if 100 div exch 100 div exch _scale astore pop iTm } def /TA { pop } def /Tq { pop } def /Tg { pop } def /TG { pop } def /Tv { /_lineorientation exch ddef } def /TV { /_charorientation exch ddef } def /Ty { dup /_yokoorientation exch ddef 1 sub neg Tv } def /TY { pop } def /T~ { Tx } def /Th { pop pop pop pop pop } def /TX { pop } def /Tk { _fontSize mul 1000 div _lineorientation 0 eq { neg 0 } { 0 exch } ifelse rmoveto pop } def /TK { 2 npop } def /T* { _leading aload pop _lineorientation 0 ne { exch } if Td } def /T*- { _leading aload pop _lineorientation 0 ne { exch } if exch neg exch neg Td } def /T- { _ax neg 0 rmoveto _lineorientation 1 eq _charorientation 0 eq and { 1 TV _hyphen Tx 0 TV } { _hyphen Tx } ifelse } def /T+ { } def /TR { _ctm currentmatrix pop _tm astore pop iTm 0 0 moveto } def /TS { currentfont 3 1 roll /_Symbol_ findfont _fontSize scalefont setfont 0 eq { Tx } { Tj } ifelse setfont } def /Xb { pop pop } def /Tb /Xb load def /Xe { pop pop pop pop } def /Te /Xe load def /XB { } def /TB /XB load def currentdict readonly pop end setpacking % /X^ { currentfont 5 1 roll dup havefont { findfont _fontSize scalefont setfont } { pop exch } ifelse 2 index 0 eq { Tx } { Tj } ifelse pop pop setfont } def /T^ /X^ load def %%EndResource %%BeginProcSet: Adobe_ColorImage_AI6 1.3 0 userdict /Adobe_ColorImage_AI6 known not { userdict /Adobe_ColorImage_AI6 53 dict put } if userdict /Adobe_ColorImage_AI6 get begin /initialize { Adobe_ColorImage_AI6 begin Adobe_ColorImage_AI6 { dup type /arraytype eq { dup xcheck { bind } if } if pop pop } forall } def /terminate { end } def currentdict /Adobe_ColorImage_AI6_Vars known not { /Adobe_ColorImage_AI6_Vars 41 dict def } if Adobe_ColorImage_AI6_Vars begin /plateindex -1 def /_newproc null def /_proc1 null def /_proc2 null def /sourcearray 4 array def /_ptispace null def /_ptiname null def /_pti0 0 def /_pti1 0 def /_ptiproc null def /_ptiscale 0 def /_pticomps 0 def /_ptibuf 0 string def /_gtigray 0 def /_cticmyk null def /_rtirgb null def /XIEnable true def /XIType 0 def /XIEncoding 0 def /XICompression 0 def /XIChannelCount 0 def /XIBitsPerPixel 0 def /XIImageHeight 0 def /XIImageWidth 0 def /XIImageMatrix null def /XIRowBytes 0 def /XIFile null def /XIBuffer1 null def /XIBuffer2 null def /XIBuffer3 null def /XIDataProc null def /XIColorSpace /DeviceGray def /XIColorValues 0 def /XIPlateList false def end /ci6colorimage /colorimage where {/colorimage get}{null} ifelse def /ci6image systemdict /image get def /ci6curtransfer systemdict /currenttransfer get def /ci6curoverprint /currentoverprint where {/currentoverprint get}{{_of}} ifelse def /ci6foureq { 4 index ne { pop pop pop false }{ 4 index ne { pop pop false }{ 4 index ne { pop false }{ 4 index eq } ifelse } ifelse } ifelse } def /ci6testplate { Adobe_ColorImage_AI6_Vars begin /plateindex -1 def /setcmykcolor where { pop gsave 1 0 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub 0 1 0 0 setcmykcolor systemdict /currentgray get exec 1 exch sub 0 0 1 0 setcmykcolor systemdict /currentgray get exec 1 exch sub 0 0 0 1 setcmykcolor systemdict /currentgray get exec 1 exch sub grestore 1 0 0 0 ci6foureq { /plateindex 0 def }{ 0 1 0 0 ci6foureq { /plateindex 1 def }{ 0 0 1 0 ci6foureq { /plateindex 2 def }{ 0 0 0 1 ci6foureq { /plateindex 3 def }{ 0 0 0 0 ci6foureq { /plateindex 5 def } if } ifelse } ifelse } ifelse } ifelse pop pop pop pop } if plateindex end } def /ci6concatprocs { /packedarray where { pop dup type /packedarraytype eq 2 index type /packedarraytype eq or }{ false } ifelse { /_proc2 exch cvlit def /_proc1 exch cvlit def _proc1 aload pop _proc2 aload pop _proc1 length _proc2 length add packedarray cvx }{ /_proc2 exch cvlit def /_proc1 exch cvlit def /_newproc _proc1 length _proc2 length add array def _newproc 0 _proc1 putinterval _newproc _proc1 length _proc2 putinterval _newproc cvx } ifelse } def /ci6istint { type /arraytype eq } def /ci6isspot { dup type /arraytype eq { dup length 1 sub get /Separation eq }{ pop false } ifelse } def /ci6spotname { dup ci6isspot {dup length 2 sub get}{pop ()} ifelse } def /ci6altspace { aload pop pop pop ci6colormake } def /ci6numcomps { dup /DeviceGray eq { pop 1 }{ dup /DeviceRGB eq { pop 3 }{ /DeviceCMYK eq { 4 }{ 1 } ifelse } ifelse } ifelse } def /ci6marksplate { dup /DeviceGray eq { pop plateindex 3 eq }{ dup /DeviceRGB eq { pop plateindex 5 ne }{ dup /DeviceCMYK eq { pop plateindex 5 ne }{ dup ci6isspot { /findcmykcustomcolor where { pop dup length 2 sub get 0.1 0.1 0.1 0.1 5 -1 roll findcmykcustomcolor 1 setcustomcolor systemdict /currentgray get exec 1 ne }{ pop plateindex 5 ne } ifelse }{ pop plateindex 5 ne } ifelse } ifelse } ifelse } ifelse } def /ci6colormake { dup ci6numcomps exch 1 index 2 add 1 roll dup 1 eq {pop}{array astore} ifelse exch } def /ci6colorexpand { dup ci6spotname exch dup ci6istint { ci6altspace exch 4 1 roll }{ 1 3 1 roll } ifelse } def /ci6colortint { dup /DeviceGray eq { 3 1 roll 1 exch sub mul 1 exch sub exch }{ dup /DeviceRGB eq { 3 1 roll {1 exch sub 1 index mul 1 exch sub exch} forall pop 3 array astore exch }{ dup /DeviceCMYK eq { 3 1 roll {1 index mul exch} forall pop 4 array astore exch }{ 3 1 roll mul exch } ifelse } ifelse } ifelse } def /ci6colortocmyk { dup /DeviceGray eq { pop 1 exch sub 0 0 0 4 -1 roll 4 array astore }{ dup /DeviceRGB eq { pop aload pop _rgbtocmyk 4 array astore }{ dup /DeviceCMYK eq { pop }{ ci6altspace ci6colortint ci6colortocmyk } ifelse } ifelse } ifelse } def /ci6makeimagedict { 7 dict begin /ImageType 1 def /Decode exch def /DataSource exch def /ImageMatrix exch def /BitsPerComponent exch def /Height exch def /Width exch def currentdict end } def /ci6stringinvert { 0 1 2 index length 1 sub { dup 2 index exch get 255 exch sub 2 index 3 1 roll put } for } def /ci6stringknockout { 0 1 2 index length 1 sub { 255 2 index 3 1 roll put } for } def /ci6stringapply { 0 1 4 index length 1 sub { dup 4 index exch get 3 index 3 1 roll 3 index exec } for pop exch pop } def /ci6walkrgbstring { 0 3 index dup length 1 sub 0 3 3 -1 roll { 3 getinterval {} forall 5 index exec 3 index } for 5 {pop} repeat } def /ci6walkcmykstring { 0 3 index dup length 1 sub 0 4 3 -1 roll { 4 getinterval {} forall 6 index exec 3 index } for 5 { pop } repeat } def /ci6putrgbtograystr { .11 mul exch .59 mul add exch .3 mul add cvi 3 copy put pop 1 add } def /ci6putcmyktograystr { exch .11 mul add exch .59 mul add exch .3 mul add dup 255 gt { pop 255 } if 255 exch sub cvi 3 copy put pop 1 add } def /ci6rgbtograyproc { Adobe_ColorImage_AI6_Vars begin sourcearray 0 get exec XIBuffer3 dup 3 1 roll /ci6putrgbtograystr load exch ci6walkrgbstring end } def /ci6cmyktograyproc { Adobe_ColorImage_AI6_Vars begin sourcearray 0 get exec XIBuffer3 dup 3 1 roll /ci6putcmyktograystr load exch ci6walkcmykstring end } def /ci6separatecmykproc { Adobe_ColorImage_AI6_Vars begin sourcearray 0 get exec XIBuffer3 0 2 index plateindex 4 2 index length 1 sub { get 255 exch sub 3 copy put pop 1 add 2 index } for pop pop exch pop end } def /ci6compositeimage { dup 1 eq { pop pop image }{ /ci6colorimage load null ne { ci6colorimage }{ 3 1 roll pop sourcearray 0 3 -1 roll put 3 eq {/ci6rgbtograyproc}{/ci6cmyktograyproc} ifelse load image } ifelse } ifelse } def /ci6knockoutimage { gsave 0 ci6curtransfer exec 1 ci6curtransfer exec eq { 0 ci6curtransfer exec 0.5 lt }{ 0 ci6curtransfer exec 1 ci6curtransfer exec gt } ifelse {{pop 0}}{{pop 1}} ifelse systemdict /settransfer get exec ci6compositeimage grestore } def /ci6drawimage { ci6testplate -1 eq { pop ci6compositeimage }{ dup type /arraytype eq { dup length plateindex gt {plateindex get}{pop false} ifelse }{ { true }{ dup 1 eq {plateindex 3 eq}{plateindex 3 le} ifelse } ifelse } ifelse { dup 1 eq { pop pop ci6image }{ dup 3 eq { ci6compositeimage }{ pop pop sourcearray 0 3 -1 roll put /ci6separatecmykproc load ci6image } ifelse } ifelse }{ ci6curoverprint { 7 {pop} repeat }{ ci6knockoutimage } ifelse } ifelse } ifelse } def /ci6proctintimage { /_ptispace exch store /_ptiname exch store /_pti1 exch store /_pti0 exch store /_ptiproc exch store /_pticomps _ptispace ci6numcomps store /_ptiscale _pti1 _pti0 sub store level2? { _ptiname length 0 gt version cvr 2012 ge and { [/Separation _ptiname _ptispace {_ptiproc}] setcolorspace [_pti0 _pti1] ci6makeimagedict ci6image }{ [/Indexed _ptispace 255 {255 div _ptiscale mul _pti0 add _ptiproc}] setcolorspace [0 255] ci6makeimagedict ci6image } ifelse }{ _pticomps 1 eq { { dup { 255 div _ptiscale mul _pti0 add _ptiproc 255 mul cvi put } ci6stringapply } ci6concatprocs ci6image }{ { dup length _pticomps mul dup _ptibuf length ne {/_ptibuf exch string store}{pop} ifelse _ptibuf { exch _pticomps mul exch 255 div _ptiscale mul _pti0 add _ptiproc _pticomps 2 add -2 roll _pticomps 1 sub -1 0 { 1 index add 2 index exch 5 -1 roll 255 mul cvi put } for pop pop } ci6stringapply } ci6concatprocs false _pticomps /ci6colorimage load null eq {7 {pop} repeat}{ci6colorimage} ifelse } ifelse } ifelse } def /ci6graytintimage { /_gtigray 5 -1 roll store {1 _gtigray sub mul 1 exch sub} 4 1 roll /DeviceGray ci6proctintimage } def /ci6cmyktintimage { /_cticmyk 5 -1 roll store {_cticmyk {1 index mul exch} forall pop} 4 1 roll /DeviceCMYK ci6proctintimage } def /ci6rgbtintimage { /_rtirgb 5 -1 roll store {_rtirgb {1 exch sub 1 index mul 1 exch sub exch} forall pop} 4 1 roll /DeviceRGB ci6proctintimage } def /ci6tintimage { ci6testplate -1 eq { ci6colorexpand 3 -1 roll 5 -1 roll {0}{0 exch} ifelse 4 2 roll dup /DeviceGray eq { pop ci6graytintimage }{ dup /DeviceRGB eq { pop ci6rgbtintimage }{ pop ci6cmyktintimage } ifelse } ifelse }{ dup ci6marksplate { plateindex 5 lt { ci6colortocmyk plateindex get dup 0 eq ci6curoverprint and { 7 {pop} repeat }{ 1 exch sub exch {1 0}{0 1} ifelse () ci6graytintimage } ifelse }{ pop exch {0}{0 exch} ifelse 0 3 1 roll () ci6graytintimage } ifelse }{ ci6curoverprint { 8 {pop} repeat }{ pop pop pop {pop 1} 0 1 () /DeviceGray ci6proctintimage } ifelse } ifelse } ifelse } def /XINullImage { } def /XIImageMask { XIImageWidth XIImageHeight false [XIImageWidth 0 0 XIImageHeight neg 0 0] /XIDataProc load imagemask } def /XIImageTint { XIImageWidth XIImageHeight XIBitsPerPixel [XIImageWidth 0 0 XIImageHeight neg 0 0] /XIDataProc load XIType 3 eq XIColorValues XIColorSpace ci6tintimage } def /XIImage { XIImageWidth XIImageHeight XIBitsPerPixel [XIImageWidth 0 0 XIImageHeight neg 0 0] /XIDataProc load false XIChannelCount XIPlateList ci6drawimage } def /XG { pop pop } def /XF { 13 {pop} repeat } def /Xh { Adobe_ColorImage_AI6_Vars begin gsave /XIType exch def /XIImageHeight exch def /XIImageWidth exch def /XIImageMatrix exch def 0 0 moveto XIImageMatrix concat XIImageWidth XIImageHeight scale /_lp /null ddef _fc /_lp /imagemask ddef end } def /XH { Adobe_ColorImage_AI6_Vars begin grestore end } def /XIEnable { Adobe_ColorImage_AI6_Vars /XIEnable 3 -1 roll put } def /XC { Adobe_ColorImage_AI6_Vars begin ci6colormake /XIColorSpace exch def /XIColorValues exch def end } def /XIPlates { Adobe_ColorImage_AI6_Vars begin /XIPlateList exch def end } def /XI { Adobe_ColorImage_AI6_Vars begin gsave /XIType exch def cvi dup 256 idiv /XICompression exch store 256 mod /XIEncoding exch store pop pop /XIChannelCount exch def /XIBitsPerPixel exch def /XIImageHeight exch def /XIImageWidth exch def pop pop pop pop /XIImageMatrix exch def XIBitsPerPixel 1 eq { XIImageWidth 8 div ceiling cvi }{ XIImageWidth XIChannelCount mul } ifelse /XIRowBytes exch def XIEnable { /XIBuffer3 XIImageWidth string def XICompression 0 eq { /XIBuffer1 XIRowBytes string def XIEncoding 0 eq { {currentfile XIBuffer1 readhexstring pop} }{ {currentfile XIBuffer1 readstring pop} } ifelse }{ /XIBuffer1 256 string def /XIBuffer2 XIRowBytes string def {currentfile XIBuffer1 readline pop (%) anchorsearch {pop} if} /ASCII85Decode filter /DCTDecode filter /XIFile exch def {XIFile XIBuffer2 readstring pop} } ifelse /XIDataProc exch def XIType 1 ne { 0 setgray } if XIType 1 eq { XIImageMask }{ XIType 2 eq XIType 3 eq or { XIImageTint }{ XIImage } ifelse } ifelse }{ XINullImage } ifelse /XIPlateList false def grestore end } def end %%EndProcSet %%BeginResource: procset Adobe_Illustrator_AI5 1.3 0 %%Title: (Adobe Illustrator (R) Version 8.0 Full Prolog) %%Version: 1.3 0 %%CreationDate: (3/7/1994) () %%Copyright: ((C) 1987-1998 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_Illustrator_AI5_vars 112 dict dup begin put /_?cmyk false def /_eo false def /_lp /none def /_pf { } def /_ps { } def /_psf { } def /_pss { } def /_pjsf { } def /_pjss { } def /_pola 0 def /_doClip 0 def /cf currentflat def /_lineorientation 0 def /_charorientation 0 def /_yokoorientation 0 def /_tm matrix def /_renderStart [ /e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0 ] def /_renderEnd [ null null null null /i1 /i1 /i1 /i1 ] def /_render -1 def /_shift [0 0] def /_ax 0 def /_ay 0 def /_cx 0 def /_cy 0 def /_leading [ 0 0 ] def /_ctm matrix def /_mtx matrix def /_sp 16#020 def /_hyphen (-) def /_fontSize 0 def /_fontAscent 0 def /_fontDescent 0 def /_fontHeight 0 def /_fontRotateAdjust 0 def /Ss 256 string def Ss 0 (fonts/) putinterval /_cnt 0 def /_scale [1 1] def /_nativeEncoding 0 def /_useNativeEncoding 0 def /_tempEncode 0 def /_pntr 0 def /_tDict 2 dict def /_hfname 100 string def /_hffound false def /Tx { } def /Tj { } def /CRender { } def /_AI3_savepage { } def /_gf null def /_cf 4 array def /_rgbf 3 array def /_if null def /_of false def /_fc { } def /_gs null def /_cs 4 array def /_rgbs 3 array def /_is null def /_os false def /_sc { } def /_pd 1 dict def /_ed 15 dict def /_pm matrix def /_fm null def /_fd null def /_fdd null def /_sm null def /_sd null def /_sdd null def /_i null def /_lobyte 0 def /_hibyte 0 def /_cproc null def /_cscript 0 def /_hvax 0 def /_hvay 0 def /_hvwb 0 def /_hvcx 0 def /_hvcy 0 def /_bitfont null def /_bitlobyte 0 def /_bithibyte 0 def /_bitkey null def /_bitdata null def /_bitindex 0 def /discardSave null def /buffer 256 string def /beginString null def /endString null def /endStringLength null def /layerCnt 1 def /layerCount 1 def /perCent (%) 0 get def /perCentSeen? false def /newBuff null def /newBuffButFirst null def /newBuffLast null def /clipForward? false def end userdict /Adobe_Illustrator_AI5 known not { userdict /Adobe_Illustrator_AI5 100 dict put } if userdict /Adobe_Illustrator_AI5 get begin /initialize { Adobe_Illustrator_AI5 dup begin Adobe_Illustrator_AI5_vars begin /_aicmykps where {pop /_?cmyk _aicmykps def}if discardDict { bind pop pop } forall dup /nc get begin { dup xcheck 1 index type /operatortype ne and { bind } if pop pop } forall end newpath } def /terminate { end end } def /_ null def /ddef { Adobe_Illustrator_AI5_vars 3 1 roll put } def /xput { dup load dup length exch maxlength eq { dup dup load dup length 2 mul dict copy def } if load begin def end } def /npop { { pop } repeat } def /hswj { dup stringwidth 3 2 roll { _hvwb eq { exch _hvcx add exch _hvcy add } if exch _hvax add exch _hvay add } cforall } def /vswj { 0 0 3 -1 roll { dup 255 le _charorientation 1 eq and { dup cstring stringwidth 5 2 roll _hvwb eq { exch _hvcy sub exch _hvcx sub } if exch _hvay sub exch _hvax sub 4 -1 roll sub exch 3 -1 roll sub exch } { _hvwb eq { exch _hvcy sub exch _hvcx sub } if exch _hvay sub exch _hvax sub _fontHeight sub } ifelse } cforall } def /swj { 6 1 roll /_hvay exch ddef /_hvax exch ddef /_hvwb exch ddef /_hvcy exch ddef /_hvcx exch ddef _lineorientation 0 eq { hswj } { vswj } ifelse } def /sw { 0 0 0 6 3 roll swj } def /vjss { 4 1 roll { dup cstring dup length 1 eq _charorientation 1 eq and { -90 rotate currentpoint _fontRotateAdjust add moveto gsave false charpath currentpoint 5 index setmatrix stroke grestore _fontRotateAdjust sub moveto _sp eq { 5 index 5 index rmoveto } if 2 copy rmoveto 90 rotate } { currentpoint _fontHeight sub 5 index sub 3 index _sp eq { 9 index sub } if currentpoint exch 4 index stringwidth pop 2 div sub exch _fontAscent sub moveto gsave 2 index false charpath 6 index setmatrix stroke grestore moveto pop pop } ifelse } cforall 6 npop } def /hjss { 4 1 roll { dup cstring gsave false charpath currentpoint 5 index setmatrix stroke grestore moveto _sp eq { 5 index 5 index rmoveto } if 2 copy rmoveto } cforall 6 npop } def /jss { _lineorientation 0 eq { hjss } { vjss } ifelse } def /ss { 0 0 0 7 3 roll jss } def /vjsp { 4 1 roll { dup cstring dup length 1 eq _charorientation 1 eq and { -90 rotate currentpoint _fontRotateAdjust add moveto false charpath currentpoint _fontRotateAdjust sub moveto _sp eq { 5 index 5 index rmoveto } if 2 copy rmoveto 90 rotate } { currentpoint _fontHeight sub 5 index sub 3 index _sp eq { 9 index sub } if currentpoint exch 4 index stringwidth pop 2 div sub exch _fontAscent sub moveto 2 index false charpath moveto pop pop } ifelse } cforall 6 npop } def /hjsp { 4 1 roll { dup cstring false charpath _sp eq { 5 index 5 index rmoveto } if 2 copy rmoveto } cforall 6 npop } def /jsp { matrix currentmatrix _lineorientation 0 eq {hjsp} {vjsp} ifelse } def /sp { matrix currentmatrix 0 0 0 7 3 roll _lineorientation 0 eq {hjsp} {vjsp} ifelse } def /pl { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } def /setstrokeadjust where { pop true setstrokeadjust /c { curveto } def /C /c load def /v { currentpoint 6 2 roll curveto } def /V /v load def /y { 2 copy curveto } def /Y /y load def /l { lineto } def /L /l load def /m { moveto } def } { /c { pl curveto } def /C /c load def /v { currentpoint 6 2 roll pl curveto } def /V /v load def /y { pl 2 copy curveto } def /Y /y load def /l { pl lineto } def /L /l load def /m { pl moveto } def } ifelse /d { setdash } def /cf { } def /i { dup 0 eq { pop cf } if setflat } def /j { setlinejoin } def /J { setlinecap } def /M { setmiterlimit } def /w { setlinewidth } def /XR { 0 ne /_eo exch ddef } def /H { } def /h { closepath } def /N { _pola 0 eq { _doClip 1 eq { _eo {eoclip} {clip} ifelse /_doClip 0 ddef } if newpath } { /CRender { N } ddef } ifelse } def /n { N } def /F { _pola 0 eq { _doClip 1 eq { gsave _pf grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _fc /_doClip 0 ddef } { _pf } ifelse } { /CRender { F } ddef } ifelse } def /f { closepath F } def /S { _pola 0 eq { _doClip 1 eq { gsave _ps grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc /_doClip 0 ddef } { _ps } ifelse } { /CRender { S } ddef } ifelse } def /s { closepath S } def /B { _pola 0 eq { _doClip 1 eq gsave F grestore { gsave S grestore _eo {eoclip} {clip} ifelse newpath /_lp /none ddef _sc /_doClip 0 ddef } { S } ifelse } { /CRender { B } ddef } ifelse } def /b { closepath B } def /W { /_doClip 1 ddef } def /* { count 0 ne { dup type /stringtype eq { pop } if } if newpath } def /u { } def /U { } def /q { _pola 0 eq { gsave } if } def /Q { _pola 0 eq { grestore } if } def /*u { _pola 1 add /_pola exch ddef } def /*U { _pola 1 sub /_pola exch ddef _pola 0 eq { CRender } if } def /D { pop } def /*w { } def /*W { } def /` { /_i save ddef clipForward? { nulldevice } if 6 1 roll 4 npop concat pop userdict begin /showpage { } def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash /setstrokeadjust where {pop false setstrokeadjust} if newpath 0 setgray false setoverprint } def /~ { end _i restore } def /_rgbtocmyk { 3 { 1 exch sub 3 1 roll } repeat 3 copy 1 4 1 roll 3 { 3 index 2 copy gt { exch } if pop 4 1 roll } repeat pop pop pop 4 1 roll 3 { 3 index sub 3 1 roll } repeat 4 -1 roll } def /setrgbfill { _rgbf astore pop /_fc { _lp /fill ne { _of setoverprint _rgbf aload pop setrgbcolor /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc hvashow } ddef /_pjsf { _fc hvawidthshow } ddef /_lp /none ddef } def /setrgbstroke { _rgbs astore pop /_sc { _lp /stroke ne { _os setoverprint _rgbs aload pop setrgbcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /O { 0 ne /_of exch ddef /_lp /none ddef } def /R { 0 ne /_os exch ddef /_lp /none ddef } def /g { /_gf exch ddef /_fc { _lp /fill ne { _of setoverprint _gf setgray /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc hvashow } ddef /_pjsf { _fc hvawidthshow } ddef /_lp /none ddef } def /G { /_gs exch ddef /_sc { _lp /stroke ne { _os setoverprint _gs setgray /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /k { _cf astore pop /_fc { _lp /fill ne { _of setoverprint _cf aload pop setcmykcolor /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc hvashow } ddef /_pjsf { _fc hvawidthshow } ddef /_lp /none ddef } def /K { _cs astore pop /_sc { _lp /stroke ne { _os setoverprint _cs aload pop setcmykcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /Xa { _?cmyk { 3 npop k }{ setrgbfill 4 npop } ifelse } def /XA { _?cmyk { 3 npop K }{ setrgbstroke 4 npop } ifelse } def /Xs { /_gf exch ddef 5 npop /_fc { _lp /fill ne { _of setoverprint _gf setAIseparationgray /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc hvashow } ddef /_pjsf { _fc hvawidthshow } ddef /_lp /none ddef } def /XS { /_gs exch ddef 5 npop /_sc { _lp /stroke ne { _os setoverprint _gs setAIseparationgray /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /Xx { exch /_gf exch ddef 0 eq { findcmykcustomcolor }{ _?cmyk {true}{/findrgbcustomcolor where{pop false}{true}ifelse}ifelse { 4 1 roll 3 npop findcmykcustomcolor }{ 8 -4 roll 4 npop findrgbcustomcolor } ifelse } ifelse /_if exch ddef /_fc { _lp /fill ne { _of setoverprint _if _gf 1 exch sub setcustomcolor /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc hvashow } ddef /_pjsf { _fc hvawidthshow } ddef /_lp /none ddef } def /XX { exch /_gs exch ddef 0 eq { findcmykcustomcolor }{ _?cmyk {true}{/findrgbcustomcolor where{pop false}{true}ifelse}ifelse { 4 1 roll 3 npop findcmykcustomcolor }{ 8 -4 roll 4 npop findrgbcustomcolor } ifelse } ifelse /_is exch ddef /_sc { _lp /stroke ne { _os setoverprint _is _gs 1 exch sub setcustomcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /x { /_gf exch ddef findcmykcustomcolor /_if exch ddef /_fc { _lp /fill ne { _of setoverprint _if _gf 1 exch sub setcustomcolor /_lp /fill ddef } if } ddef /_pf { _fc _eo {eofill} {fill} ifelse } ddef /_psf { _fc hvashow } ddef /_pjsf { _fc hvawidthshow } ddef /_lp /none ddef } def /X { /_gs exch ddef findcmykcustomcolor /_is exch ddef /_sc { _lp /stroke ne { _os setoverprint _is _gs 1 exch sub setcustomcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /XK { 3 -1 roll pop 0 eq { 1 exch sub 3 {dup 3 1 roll mul 5 1 roll} repeat mul 4 1 roll K } { 1 exch sub 4 1 roll 3 {1 exch sub 3 index mul 1 exch sub 3 1 roll} repeat 4 -1 roll pop XA } ifelse } def /Xk { 3 -1 roll pop 0 eq { 1 exch sub 3 {dup 3 1 roll mul 5 1 roll} repeat mul 4 1 roll k } { 1 exch sub 4 1 roll 3 {1 exch sub 3 index mul 1 exch sub 3 1 roll} repeat 4 -1 roll pop Xa } ifelse } def /A { pop } def /annotatepage { userdict /annotatepage 2 copy known {get exec} {pop pop} ifelse } def /XT { pop pop } def /Xt { pop } def /discard { save /discardSave exch store discardDict begin /endString exch store gt38? { 2 add } if load stopped pop end discardSave restore } bind def userdict /discardDict 7 dict dup begin put /pre38Initialize { /endStringLength endString length store /newBuff buffer 0 endStringLength getinterval store /newBuffButFirst newBuff 1 endStringLength 1 sub getinterval store /newBuffLast newBuff endStringLength 1 sub 1 getinterval store } def /shiftBuffer { newBuff 0 newBuffButFirst putinterval newBuffLast 0 currentfile read not { stop } if put } def 0 { pre38Initialize mark currentfile newBuff readstring exch pop { { newBuff endString eq { cleartomark stop } if shiftBuffer } loop } { stop } ifelse } def 1 { pre38Initialize /beginString exch store mark currentfile newBuff readstring exch pop { { newBuff beginString eq { /layerCount dup load 1 add store } { newBuff endString eq { /layerCount dup load 1 sub store layerCount 0 eq { cleartomark stop } if } if } ifelse shiftBuffer } loop } if } def 2 { mark { currentfile buffer {readline} stopped { % assume error was due to overfilling the buffer }{ not { stop } if endString eq { cleartomark stop } if }ifelse } loop } def 3 { /beginString exch store /layerCnt 1 store mark { currentfile buffer {readline} stopped { % assume error was due to overfilling the buffer }{ not { stop } if dup beginString eq { pop /layerCnt dup load 1 add store } { endString eq { layerCnt 1 eq { cleartomark stop } { /layerCnt dup load 1 sub store } ifelse } if } ifelse }ifelse } loop } def end userdict /clipRenderOff 15 dict dup begin put { /n /N /s /S /f /F /b /B } { { _doClip 1 eq { /_doClip 0 ddef _eo {eoclip} {clip} ifelse } if newpath } def } forall /Tr /pop load def /Bb {} def /BB /pop load def /Bg {12 npop} def /Bm {6 npop} def /Bc /Bm load def /Bh {4 npop} def end /Lb { 6 npop 7 2 roll 5 npop 0 eq { 0 eq { (%AI5_BeginLayer) 1 (%AI5_EndLayer--) discard } { /clipForward? true def /Tx /pop load def /Tj /pop load def currentdict end clipRenderOff begin begin } ifelse } { 0 eq { save /discardSave exch store } if } ifelse } bind def /LB { discardSave dup null ne { restore } { pop clipForward? { currentdict end end begin /clipForward? false ddef } if } ifelse } bind def /Pb { pop pop 0 (%AI5_EndPalette) discard } bind def /Np { 0 (%AI5_End_NonPrinting--) discard } bind def /Ln /pop load def /Ap /pop load def /Ar { 72 exch div 0 dtransform dup mul exch dup mul add sqrt dup 1 lt { pop 1 } if setflat } def /Mb { q } def /Md { } def /MB { Q } def /nc 4 dict def nc begin /setgray { pop } bind def /setcmykcolor { 4 npop } bind def /setrgbcolor { 3 npop } bind def /setcustomcolor { 2 npop } bind def currentdict readonly pop end /XP { 4 npop } bind def /XD { pop } bind def end setpacking %%EndResource %%BeginResource: procset Adobe_cshow 2.0 8 %%Title: (Writing System Operators) %%Version: 2.0 8 %%CreationDate: (1/23/89) () %%Copyright: ((C) 1992-1996 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_cshow 14 dict dup begin put /initialize { Adobe_cshow begin Adobe_cshow { dup xcheck { bind } if pop pop } forall end Adobe_cshow begin } def /terminate { currentdict Adobe_cshow eq { end } if } def /cforall { /_lobyte 0 ddef /_hibyte 0 ddef /_cproc exch ddef /_cscript currentfont /FontScript known { currentfont /FontScript get } { -1 } ifelse ddef { /_lobyte exch ddef _hibyte 0 eq _cscript 1 eq _lobyte 129 ge _lobyte 159 le and _lobyte 224 ge _lobyte 252 le and or and _cscript 2 eq _lobyte 161 ge _lobyte 254 le and and _cscript 3 eq _lobyte 161 ge _lobyte 254 le and and _cscript 25 eq _lobyte 161 ge _lobyte 254 le and and _cscript -1 eq or or or or and { /_hibyte _lobyte ddef } { _hibyte 256 mul _lobyte add _cproc /_hibyte 0 ddef } ifelse } forall } def /cstring { dup 256 lt { (s) dup 0 4 3 roll put } { dup 256 idiv exch 256 mod (hl) dup dup 0 6 5 roll put 1 4 3 roll put } ifelse } def /clength { 0 exch { 256 lt { 1 } { 2 } ifelse add } cforall } def /hawidthshow { { dup cstring show _hvax _hvay rmoveto _hvwb eq { _hvcx _hvcy rmoveto } if } cforall } def /vawidthshow { { dup 255 le _charorientation 1 eq and { -90 rotate 0 _fontRotateAdjust rmoveto cstring _hvcx _hvcy _hvwb _hvax _hvay 6 -1 roll awidthshow 0 _fontRotateAdjust neg rmoveto 90 rotate } { currentpoint _fontHeight sub exch _hvay sub exch _hvax sub 2 index _hvwb eq { exch _hvcy sub exch _hvcx sub } if 3 2 roll cstring dup stringwidth pop 2 div neg _fontAscent neg rmoveto show moveto } ifelse } cforall } def /hvawidthshow { 6 1 roll /_hvay exch ddef /_hvax exch ddef /_hvwb exch ddef /_hvcy exch ddef /_hvcx exch ddef _lineorientation 0 eq { hawidthshow } { vawidthshow } ifelse } def /hvwidthshow { 0 0 3 -1 roll hvawidthshow } def /hvashow { 0 0 0 6 -3 roll hvawidthshow } def /hvshow { 0 0 0 0 0 6 -1 roll hvawidthshow } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_shading_AI8 1.0 0 %%Title: (Adobe Illustrator 8 Shading Procset) %%Version: 1.0 0 %%CreationDate: (12/17/97) () %%Copyright: ((C) 1987-1997 Adobe Systems Incorporated All Rights Reserved) userdict /defaultpacking currentpacking put true setpacking userdict /Adobe_shading_AI8 10 dict dup begin put /initialize { Adobe_shading_AI8 begin Adobe_shading_AI8 bdprocs Mesh /initialize get exec } def /terminate { currentdict Adobe_shading_AI8 eq { end } if } def /bdprocs { { dup xcheck 1 index type /arraytype eq and { bind } if pop pop } forall } def /X! {pop} def /X# {pop pop} def /Mesh 40 dict def Mesh begin /initialize { Mesh bdprocs Mesh begin /emulate? /AI8MeshEmulation where { pop AI8MeshEmulation }{ systemdict /shfill known not } ifelse def end } def /bd { shadingdict begin } def /paint { emulate? { end }{ /_lp /none ddef _fc /_lp /none ddef /AIColorSpace AIColorSpace tocolorspace store /ColorSpace AIColorSpace topsspace store version_ge_3010.106 not systemdict /setsmoothness known and { 0.0001 setsmoothness } if composite? { /DataSource getdatasrc def Matrix concat currentdict end shfill }{ AIColorSpace makesmarks AIPlateList markingplate and not isoverprint and { end }{ /ColorSpace /DeviceGray store /Decode [0 1 0 1 0 1] store /DataSource getplatesrc def Matrix concat currentdict end shfill } ifelse } ifelse } ifelse } def /shadingdict 12 dict def shadingdict begin /ShadingType 6 def /BitsPerCoordinate 16 def /BitsPerComponent 8 def /BitsPerFlag 8 def end /datafile null def /databuf 256 string def /dataptr 0 def /srcspace null def /srcchannels 0 def /dstchannels 0 def /dstplate 0 def /srctodstcolor null def /getplatesrc { /srcspace AIColorSpace store /srcchannels AIColorSpace getnchannels store /dstchannels 1 store /dstplate getplateindex store /srctodstcolor srcspace makesmarks { dstplate 4 eq { {1 exch sub} }{ {srcspace tocmyk 3 dstplate sub index 1 exch sub 5 1 roll 4 {pop} repeat} } ifelse }{ {srcchannels {pop} repeat 1} } ifelse store /datafile getdatasrc store /rdpatch168 load DataLength () /SubFileDecode filter } def /getdatasrc { /rdcmntline load /ASCII85Decode filter } def /rdpatch168 { /dataptr 0 store 49 rdcount 4 { dup {pop srcchannels getint8} if dup {pop srctodstcolor dstchannels putint8 true} if } repeat {databuf 0 dataptr getinterval}{()} ifelse } def /rdpatch3216 { /dataptr 0 store 97 rdcount 4 { dup {pop srcchannels getint16} if dup {pop srctodstcolor dstchannels putint16 true} if } repeat {databuf 0 dataptr getinterval}{()} ifelse } def /rdcount { dup 0 gt { datafile databuf dataptr 4 -1 roll getinterval readstring exch length dataptr add /dataptr exch store }{ true } ifelse } def /getint8 { mark true 3 -1 roll { dup {pop datafile read} if dup {pop 255 div true} if } repeat { counttomark 1 add -1 roll pop true }{ cleartomark false } ifelse } def /putint8 { dup dataptr add /dataptr exch store dataptr exch { 1 sub exch 255 mul cvi databuf 2 index 3 -1 roll put } repeat pop } def /getint16 { mark true 3 -1 roll { dup {pop datafile read} if dup {pop 256 mul datafile read} if dup {pop add 65535 div true} if } repeat { counttomark 1 add -1 roll pop true }{ cleartomark false } ifelse } def /putint16 { dup 2 mul dataptr add /dataptr exch store dataptr exch { 2 sub exch 65535 mul cvi dup 256 idiv databuf 3 index 3 -1 roll put 256 mod databuf 2 index 1 add 3 -1 roll put } repeat pop } def /srcbuf 256 string def /rdcmntline { currentfile srcbuf readline pop (%) anchorsearch {pop} if } def /getplateindex { 0 [cyan? magenta? yellow? black? customColor?] {{exit} if 1 add} forall } def /aicsarray 4 array def /aicsaltvals 4 array def /aicsaltcolr aicsaltvals def /tocolorspace { dup type /arraytype eq { mark exch aload pop aicsarray 0 3 -1 roll put aicsarray 1 3 -1 roll put dup aicsarray 2 3 -1 roll put gettintxform aicsarray 3 3 -1 roll put counttomark aicsaltvals 0 3 -1 roll getinterval /aicsaltcolr exch store aicsaltcolr astore pop pop aicsarray } if } def /subtintxform {aicsaltcolr {1 index mul exch} forall pop} def /addtintxform {aicsaltcolr {1 sub 1 index mul 1 add exch} forall pop} def /gettintxform { /DeviceRGB eq {/addtintxform}{/subtintxform} ifelse load } def /getnchannels { dup type /arraytype eq {0 get} if colorspacedict exch get begin Channels end } def /makesmarks { composite? { pop true }{ dup dup type /arraytype eq {0 get} if colorspacedict exch get begin MarksPlate end } ifelse } def /markingplate { composite? { pop true }{ dup type /arraytype eq { dup length getplateindex gt {getplateindex get}{pop false} ifelse } if } ifelse } def /tocmyk { dup dup type /arraytype eq {0 get} if colorspacedict exch get begin ToCMYK end } def /topsspace { dup dup type /arraytype eq {0 get} if colorspacedict exch get begin ToPSSpace end } def /colorspacedict 5 dict dup begin /DeviceGray 4 dict dup begin /Channels 1 def /MarksPlate {pop black?} def /ToCMYK {pop 1 exch sub 0 0 0 4 -1 roll} def /ToPSSpace {} def end def /DeviceRGB 4 dict dup begin /Channels 3 def /MarksPlate {pop isCMYKSep?} def /ToCMYK {pop _rgbtocmyk} def /ToPSSpace {} def end def /DeviceCMYK 4 dict dup begin /Channels 4 def /MarksPlate {pop isCMYKSep?} def /ToCMYK {pop} def /ToPSSpace {} def end def /Separation 4 dict dup begin /Channels 1 def /MarksPlate { /findcmykcustomcolor where { pop dup 1 exch ToCMYK 5 -1 roll 1 get findcmykcustomcolor 1 setcustomcolor systemdict /currentgray get exec 1 ne }{ pop false } ifelse } def /ToCMYK { dup 2 get mark exch 4 2 roll 3 get exec counttomark -1 roll tocmyk 5 -1 roll pop } def /ToPSSpace {} def end def /Process 4 dict dup begin /Channels 1 def /MarksPlate { isCMYKSep? { 1 exch ToCMYK 4 array astore getplateindex get 0 ne }{ pop false } ifelse } def /ToCMYK { dup 2 get mark exch 4 2 roll 3 get exec counttomark -1 roll tocmyk 5 -1 roll pop } def /ToPSSpace { 4 array copy dup 0 /Separation put } def end def end def /isoverprint { /currentoverprint where {pop currentoverprint}{_of} ifelse } def /version_ge_3010.106 { version {cvr} stopped { pop false }{ 3010.106 ge } ifelse } def end end defaultpacking setpacking %%EndResource %%EndProlog %%BeginSetup %%IncludeFont: Times-Italic userdict /_useSmoothShade false put userdict /_aicmykps true put userdict /_forceToCMYK true put Adobe_level2_AI5 /initialize get exec Adobe_cshow /initialize get exec Adobe_Illustrator_AI5_vars Adobe_Illustrator_AI5 Adobe_typography_AI5 /initialize get exec Adobe_ColorImage_AI6 /initialize get exec Adobe_shading_AI8 /initialize get exec Adobe_Illustrator_AI5 /initialize get exec [ 39/quotesingle 96/grave 130/quotesinglbase/florin/quotedblbase/ellipsis /dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE 145/quoteleft /quoteright/quotedblleft/quotedblright/bullet/endash/emdash/tilde/trademark /scaron/guilsinglright/oe/dotlessi 159/Ydieresis /space 164/currency 166/brokenbar 168/dieresis/copyright/ordfeminine 172/logicalnot/hyphen/registered/macron/ring /plusminus/twosuperior/threesuperior/acute/mu 183/periodcentered/cedilla /onesuperior/ordmasculine 188/onequarter/onehalf/threequarters 192/Agrave /Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute /Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde /Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave /Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute /acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex /edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute /ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex /udieresis/yacute/thorn/ydieresis TE %AI55J_Tsume: None %AI3_BeginEncoding: _Times-Italic Times-Italic [/_Times-Italic/Times-Italic 0 0 1 TZ %AI3_EndEncoding AdobeType %AI5_Begin_NonPrinting Np %AI3_BeginPattern: (Bl\344tter) (Bl\344tter) 0 0 64.0781 78.9336 [ %AI3_Tile (0 O 0 R 0.05 0.2 1 0 k 0.05 0.2 1 0 K ) @ ( %AI6_BeginPatternLayer 800 Ar 0 J 0 j 1 w 4 M []0 d %AI3_Note: 0 D 0 XR 64.0781 78.9336 m 64.0781 0 L 0 0 L 0 78.9336 L 64.0781 78.9336 L f %AI6_EndPatternLayer ) & (0 O 0 R 0.83 0 1 0 k 0.83 0 1 0 K ) @ ( %AI6_BeginPatternLayer 800 Ar 0 J 0 j 1 w 4 M []0 d 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EndOfTheIncludedPostscriptMagicCookie % Finally, here is the rest of gelfreich_mp_arc_2002.tex: %-n % %\documentclass[12pt]{article} % V. Gelfreich % Jan. 2002 \usepackage{amsfonts} \usepackage{graphicx} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% definitions %% \newcommand\x{\underline{x}} \renewcommand\d{\mathrm{d}} \renewcommand\i{\mathrm{i}} \newcommand\e{\mathrm{e}} \newcommand\tfrac[2]{{\textstyle{\frac{{#1}}{{#2}}}}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \title {Chaotic zone in the Bogdanov-Takens bifurcation for diffeomorphisms \protect\footnote{Mathematical Physics Preprint Archive, January 2002, \newline {\tt http://www.ma.utexas.edu/mp\_arc}} } \author{Vassili Gelfreich\\ \normalsize Institut f\"ur Mathematik I, Freie Universit\"at Berlin,\\ \normalsize Arnimallee 2--6, 14195 Berlin, Germany\\ \normalsize gelf@math.fu-berlin.de} \date{January 14, 2002} \begin{document} \maketitle \begin{abstract} We consider a two-parametric analytic family of diffeomorphisms near the Bogdanov-Takens bifurcation. It is known that if the parameters belong to a homoclinic zone, the map has homoclinic points. The width of the homoclinic zone is exponentially small. We derive an asymptotic formula for the width of the homoclinic zone. An analytic invariant associated with a parabolic fixed point is an important ingredient of this formula. The proof of the asymptotic formula is not complete. Additionally we provide results of computations of the invariant for model families. \end{abstract} \begin{center} Keywords: Bogdanov-Takens bifurcation, homoclinic orbits, exponentially small phenomena \end{center} \section{Introduction} There is a remarkable similarity between bifurcations of equilibria for planar vector fields and bifurcations of periodic orbits for 3 dimensional vector fields. This similarity is due to the fact that in many cases the Poincar\'e map near a bifurcating periodic orbit can be formally written as a time-$1$ map of a planar vector field. Although all Taylor coefficients of the interpolating vector field can be determined, there is no reason to expect convergence of the corresponding series since the dynamics in the 3 dimensional space can be much richer than the dynamics on the plane. On the other hand the interpolating planar vector field can be used to construct normal forms for bifurcations of the periodic orbits. Thus the difference between these two different types of bifurcations is moved beyond all algebraic orders. In real-analytic theory this difference is typically exponentially small \cite{BroerR2001,FontichS1990,Gelfreich2000}. The Bogdanov-Takens bifurcation \cite{Bogdanov1975,Takens1974,ChowLW1994} has codimension 2. In the case of a planar vector field it corresponds to an equilibrium with two vanishing eigenvalues. In the case of a periodic orbit in the 3 dimensional space both multipliers of the periodic orbit equal $1$. It is more convenient to study two dimensional Poincar\'e maps instead of 3 dimensional vector fields. The Bogdanov-Takens bifurcation for planar diffeomorphisms has been intensively studied in the recent time \cite{BroerRS1996,BroerR2001}. It was shown that, similar to planar vector fields, there are both Hopf and homoclinic bifurcations in a neighborhood of the Bogdanov-Takens bifurcation. In the vector field case the values of parameters, which correspond to the homoclinic bifurcations, form a line on the plane of parameters. In the case of diffeomorphisms transversal homoclinic orbits are possible. The latter are stable with respect to small changes of parameters, so one can expect that there is a sector (instead of the line) on the parameter plane, where the map has homoclinic points. We call this sector a {\em homoclinic zone}. An exponentially small upper bound for its width was established in \cite{BroerR2001}. The aim of this paper is to present a lower bound. Of course this lower bound is exponentially small, and we conjecture that it is positive for a generic map. In order to prove this conjecture it is necessary to show that a certain constant $\Theta$ (see Section~\ref{Se:theta}) does not vanish. We checked this conjecture numerically for several examples. Let us formulate our main result more precisely. We consider a two-parametric analytic family $F_{\mu\nu}:(x,y)\mapsto(x_1,y_1)$: \begin{equation}\label{Eq:nfl} \begin{array}{rcl} x_1&=&x+y,\\ y_1&=&y+f(x,y,\mu,\nu) \end{array} \end{equation} with analytic $f$. We assume $f$ to be of the form \begin{equation}\label{Eq:f} f(x,y,\mu,\nu)=-\mu+x^2+\nu y+\gamma xy+\dots \end{equation} It is convenient to order terms of Taylor series according to values of the calibration function, which assigns orders to monomials: $$ \delta(\mu^j\nu^kx^ly^m)=4 j+2k+2l+3m. $$ The coefficients $\mu$, $\nu$ and $\gamma$ are invariant under close-to-identity transformations, which preserve the form of the map $F_{\mu\nu}$. \begin{figure} \begin{center} \includegraphics{gelfreich_fig_1.eps} \end{center} \caption{Bifurcation diagram} \label{Fig:bifdiag} \end{figure} This form of the map is not exceptional: a generic two-parametric family of maps near its Bogdanov-Takens bifurcation can be transformed to the form (\ref{Eq:nfl}), (\ref{Eq:f}) by a change of coordinates and parameters~\cite{BroerRS1996}. \smallskip If $\mu=\nu=0$ the map $F_{\mu\nu}$ has a parabolic fixed point at the origin. Following \cite{BroerRS1996,BroerR2001} we study study the bifurcation of this point on the plane of $(\mu,\nu)$. The corresponding bifurcation diagram is shown on Fig.~\ref{Fig:bifdiag}. If a point $(\mu,\nu)$ is situated between the lines $\nu=\nu_-(\mu)$ and $\nu=\nu_+(\mu)$, $0<\mu<\mu_0$, then the map $F_{\mu\nu}$ has a homoclinic trajectory. On the lower and upper boundary the homoclinic trajectory disappears. The first and the last homoclinic points are shown on Fig.~\ref{Fig:tangent}. The pictures correspond to $\nu=\nu_-(\mu)$ and $\nu=\nu_+(\mu)$ respectively. It is not very difficult to show that $\nu_\pm(\mu)=\frac57(\gamma-2)\mu^{1/2}+O(\mu^{3/4})$. A much more difficult problem is to prove the following estimate: \begin{equation}\label{Eq:mainas} \nu_+(\mu)- \nu_-(\mu)= \frac{A_\gamma} {\mu^{5/4}} \cdot \e^{-\sqrt2\pi/\root 4 \of {\mu}}, \end{equation} \begin{equation} A_\gamma= \frac{ 5|\Theta|}{6\sqrt2}\,\e^{-6\pi^2(\gamma-2)/7}+O(\mu^{1/4}\log\mu). \end{equation} Here $\Theta$ is a constant defined later in Section~\ref{Se:theta}. It depends on $\gamma$ and on all other Taylor coefficients of the function $f(x,y,0,0)$. If the map $F_{00}$ is exactly the time-$1$ map of a planar flow, the corresponding constant $\Theta$ vanishes. Each $F_{00}$ can be interpolated by a flow up to an error, which is smaller than any power of $x$ and $y$. Thus all Taylor coefficients of $f(x,y,0,0)$ are relevant for $\Theta$. \begin{figure} \begin{center} \includegraphics{gelfreich_fig_2.eps} \end{center} \caption{The first and last homoclinic points of the map $F_{\mu\nu}$} \label{Fig:tangent} \end{figure} The formula (\ref{Eq:mainas}) implies a lower bound for the width of the zone provided $\Theta$ does not vanish. It was proved analytically that $\Theta$ does not vanish in the cases of the H\'enon family \cite{GelfreichS2001}; numerically $|\Theta(\mbox{H\'enon})|=2.47\ldots\cdot 10^6$. One should expect that $\Theta$ does not vanish generically, since it depends analytically on $F_{00}$. We recall that the {H\'enon map} \begin{eqnarray*} u_1&=&v,\\ v_1&=&a v^2-b u+1 \end{eqnarray*} can be transformed to the form (\ref{Eq:nfl}) with $$ f(x,y,\mu,\nu) = (x+y)^2-\mu +\nu y. $$ The coefficients $\mu$ and $\nu$ are in one-to-one correspondence with the original parameters: $$ a=(1+\nu/2)^2-\mu, \qquad b=1+\nu. $$ The H\'enon family has the special property: it is area-preserving for $\nu=0$. The separatrices of the area-preserving H\'enon map split transversally \cite{Gelfreich2000,GelfreichS2001,Chernov2001}. \medskip The rest of the paper contains an informal derivation of the asymptotic formula (\ref{Eq:mainas}). It can not be considered as a complete proof. The approach is based on Lazutkin's method originally proposed for a study of the standard map \cite{Lazutkin1984,Gelfreich1999}. Section~\ref{Se:numerics} provides a summary of numerical experiments used to evaluate the splitting constant $\Theta$ for some model families and to check the correctness of the asymptotic formula (\ref{Eq:mainas}). \section{Formal interpolation by a flow\label{Se:interpol}} In this section we discuss the formal interpolation of the family $F_{\mu\nu}$ by an autonomous vector-field $$ X=X^1\partial_x+X^2\partial_y, $$ where $\partial_x$ and $\partial_y$ stand for derivatives in $x$ and $y$ respectively; $X^1$ and $X^2$ are power series in $x,y,\mu$ and $\nu$. The vector field is a differential operator and can be expanded into a sum of homogeneous operators: $$ X=\sum_{k\ge1}X_k, $$ where $X_k$ increases the order of a $\delta$-homogeneous polynomial by $k$. It is not too difficult to check that there is a unique formal vector-field, such that $$ F_{\mu\nu}(\x)=\mathrm e^X\x,\qquad \x=(x,y)^T. $$ In general one expects that the series for $X$ diverges. Comparing the first two orders of the series on both sides we obtain \begin{eqnarray*} X_1&=&y\partial_x+(x^2-\mu)\partial_y,\\ X_2&=&-\tfrac12(x^2-\mu)\partial_x+(\nu+(\gamma-1)x)y\partial_y. \end{eqnarray*} The first oder vector-field $X_1$ is Hamiltonian with the Hamiltonian function $$ h_0=\frac{y^2}2+\mu x-\frac{x^3}3. $$ If $\mu>0$ it has a homoclinic loop defined by $h_0(x,y)=\frac23\mu^{3/2}$. The perturbation by $X_2$ can destroy this loop. Let us study the homoclinic bifurcation of the vector field $X_1+X_2$ using the Melnikov method \cite{GuckenheimerH1983}. The unperturbed homoclinic orbit can be find explicitly: \begin{eqnarray*} x _0(t,\mu)&=&\sqrt\mu\left( 1-\frac3{\cosh^2(t\root4\of\mu/\sqrt2)}\right),\\ y_0(t,\mu)&=&\dot x_0= 3\sqrt2\mu^{3/4}\frac{\sinh(t\root4\of\mu/\sqrt2)} {\cosh^3(t\root4\of\mu/\sqrt2)}\;. \end{eqnarray*} The Melnikov function describes the distance between the stable and unstable separatrices of the flow generated by $X_1+X_2$ measured in units of $h_0$: \begin{eqnarray*} M(\mu,\nu)&=& \int_{-\infty}^{+\infty} \left.(X_2h_0)\right|_{x_0(t),y_0(t)}\,\d t \\ &=&(\gamma-2)\int_{-\infty}^{+\infty} x_0(t)y_0^2(t)\,\d t+ \nu \int_{-\infty}^{+\infty} y_0^2(t)\,\d t. \end{eqnarray*} It is not too difficult to calculate this integral explicitly: $$ M(\mu,\nu)=\frac{24\sqrt2}{35}\, \mu^{5/4} \left(-5(\gamma-2)\sqrt\mu+7\nu \right). $$ The Melnikov function vanishes along the line $\nu=5(\gamma-2)\sqrt\mu/7$, which gives an asymptotic of the actual line of homoclinic bifurcations. In the following we will need the following derivative: \begin{equation} \frac{\partial M }{\partial \nu} (\mu,\nu) =\frac{24\sqrt2}{5} \mu^{5/4}, \end{equation} which describes how fast the distance between separatrices changes as a function of $\nu$ for a fixed $\mu$. \smallskip Of course, Melnikov-type computations do not give the width of the homoclinic zone for the map $F_{\mu\nu}$, because for a flow it reduces to a line. \smallskip Let $\nu=5(\gamma-2)\sqrt\mu/7$ and find the first correction to the unperturbed homoclinic: $x=x_0(t)+x_1(t)+\ldots$, $y=y_0(t)+y_1(t)+\ldots$ We have \begin{eqnarray*} \dot x_1&=&y_1-\tfrac12 (x_0^2-\mu),\\ \dot y_1&=&2 x_0 x_1+(\gamma-1)x_0 y_0+\nu y_0. \end{eqnarray*} For the purposes of the the present paper it is sufficient to compute $x_1$ only: $$ x_1(t)=\tfrac37(\gamma-2)y_0(t)\log\left(\sqrt\mu-x_0(t)\right). $$ This calculation can be continued and approximations for the separatrix loop for all $\delta$-orders can be constructed. All these approximations give a closed homoclinic loop. In order to detect the exponentially small splitting of separatrices we analytically continue in $t$ and study the approximations of the separatrices near a complex singularity. It is clear that $x_0$ and $x_1$ have a common singularity at $t=\pm\i\rho$ with \begin{equation}\label{Eq:rho} \rho= \frac{\pi}{\sqrt2\mu^{1/4}}\;. \end{equation} Both $x_0$ and $x_1$ are analytic in the complex strip $|\Im t|<\rho$. The main parts of $x_0$ and $x_1$ at the singularity are: \begin{equation}\label{Eq:mainsing} \begin{array}{rcl} x_0(t)&=&\displaystyle\frac6{(t-\i\rho)^2}+O(1)\;,\\ x_1(t)&=&\displaystyle\tfrac{36}{7}(\gamma-2) \frac{\i\pi+\log 6-\log(t-\i\rho)^2}{(t-\i\rho)^3} +O\left((t-\i\rho)^{-1}\right)\;. \end{array} \end{equation} We will use this expansions for the complex matching method described later in Section~\ref{Se:flowbox}. \section{Splitting constant $\Theta$\label{Se:theta}} Let us consider the map $F_{0}\equiv F_{00}$, which has a parabolic fixed point at the origin. The fixed point has stable and unstable invariant manifold, which we parameterize by solutions of the finite-difference equation: $$ \x_0^\pm(\tau+1)=F_0(\x_0^\pm(\tau)). $$ We supply this equation with asymptotic boundary conditions for the first components of $\x_0^+$ and $\x_0^-$: \begin{equation}\label{Eq:asimp0} x_0^\pm(\tau)=\frac{6}{\tau^2}-\tfrac{36}{7}(\gamma-2)\frac{\log\tau^2}{\tau^3} +O\left(\tau^{-4}\log^2\tau\right). \end{equation} The unstable solution $\x_0^-$ is analytic in a sectorial domain $$ D_-=\{\,\tau\in\mathbb C: \delta<\arg(\tau+c)<2\pi-\delta\,\} $$ with $\delta\in(0,\frac{\pi}2)$ and sufficiently large $c>0$. The stable solution $\x_0^+$ is analytic in the domain $D_+$, which is a reflection of $D_-$ with respect to the imaginary axis. These conditions define $\x_0^+$ and $\x_0^-$ uniquely. Consider the auxiliary scalar equation $$ w_0(\tau+1)=J_0(\tau)w_0(\tau), \qquad \mbox{where $J_0(\tau)=\det F_0'(\x_0^-(\tau))$.} $$ In $D_-$ this linear finite-difference equation has a unique analytic solution, which satisfies the asymptotic boundary condition $w_0(\tau)=1+o(\tau^{-1})$. Then $$ \Theta= \lim_{\Im\tau\to-\infty}\e^{2\pi\i\tau}\frac{\tilde\theta(\tau)}{w_0(\tau)} $$ gives the same value of $\Theta$; but the expression under the limit sign converges exponentially as $|\Im\tau|\to-\infty$. Let us define the splitting function \begin{equation}\label{Eq:tildetheta} \tilde\theta(\tau)= \frac1{w_0(\tau)} \det\left(\frac{\d \x_0^-}{\d\tau}(\tau);\ \x_0^+(\tau)-\x_0^-(\tau)\right) \end{equation} for $\tau\in\Omega_-$, the lower component of $D_-\cap D_+$. Then the splitting constant $\Theta$ is defined by $$ \Theta=\lim_{\Im\tau\to-\infty}\e^{2\pi\i\tau}\tilde\theta(\tau). $$ This definition generalizes the definition from \cite{Gelfreich2000}. The existence of the limit can be proved by methods of \cite{Gelfreich1999,GelfreichS2001}. Given a map $F_0$, the constant $\Theta$ can be numerically computed directly from the definition. Finally we rewrite the definition of $\Theta$ in the form \begin{equation}\label{Eq:approxtheta} \tilde\theta(\tau)\approx w_0(\tau)\Theta\,\e^{-2\pi\i\tau} \end{equation} in oder to use it later in Section~\ref{Se:flowbox}. \section{Flow box theorem\label{Se:flowbox}} Now let us come back to the study of separatrices of the original map $F_{\mu\nu}$. We assume that parameters $\mu$ and $\nu$ are both small and close to the unperturbed homoclinic line $\nu=\frac57(\gamma-2)\mu^{1/2}$. So the stable and unstable separatrices of the map are close to each other. We parameterize the stable and unstable separatrices of its hyperbolic fixed point by solutions of finite-difference equation $$ \x^{u,s}(t+1)=F_{\mu\nu}(\x^{u,s}(t)), $$ which satisfy appropriate boundary conditions \cite{Gelfreich1999,Gelfreich2000}. These functions are close to the separatrix solution of the differential equations of Section~\ref{Se:interpol}. In a neighborhood of the first intersection of the curve $\x^u(t)$ with the $y$-axes we introduce the time-energy coordinates $(E,T)$ \cite{Gelfreich1996}. In these coordinates the map $F_{\mu\nu}$ takes the form of the translation $$ (E,T)\mapsto(E,T+1). $$ The coordinates can be normalized in such a way that $$ E(\x^u(t))=0,\qquad T(\x^u(t))= t. $$ Moreover the energy $E$ is close to the Hamiltonian function $h_0$. In the $(E,T)$ coordinates a segment of the stable manifold is a graph of a periodic function $E=A(T,\mu,\nu)$, $A(T+1,\mu,\nu)=A(T,\mu,\nu)$. We can expand this function in Fourier series $$ A(T,\mu,\nu)=A_0(\mu,\nu)+A_1(\mu,\nu)\sin 2\pi (T-T_0(\mu,\nu))+h.o.t. $$ In \cite{Gelfreich1996} it was shown the h.o.t. is an exponentially small quantity of higher order. The zeroes of $A(T,\mu,\nu)$ correspond to homoclinic points. Moreover, if this function have nor zeroes, it can be shown that the separatrices do not intersect at all. The first term $A_0$ is approximated by the Melnikov function described in Section~\ref{Se:interpol}: $$ A_0(\mu,\nu)=M(\mu,\nu)+O(\mu^{2}). $$ The amplitude $A_1$ of the second term is exponentially small. The product $A_1\sin2\pi T$ can be large for non-real $T$. In order to approximate it we use the following complex matching method. We expand $E(\x^s(t))-E(\x^u(t))$ in powers of $\x^s(t)-\x^u(t)$ and use $$ \partial_x E(\x^u(t))=\frac{\dot{y}^u(t)}{w(t)},\qquad \partial_y E(\x^u(t))=-\frac{\dot{x}^u(t)}{w(t)}, $$ where $1/w(t)$ is the Jacobian of the map $(x,y)\mapsto(E,T)$ computed at the point $\x^u(t)$. We obtain that \begin{equation}\label{Eq:sgraph} A(t,\mu,\nu)=\frac1{w(t)} \det(\dot {\x}^u(t);\x^s(t)-\x^u(t))+O(|\x^s(t)-\x^u(t)|^2)\;. \end{equation} In oder to approximate this function we consider its analytic continuation in the variable $t$. The functions $\x^u(t)$ and $\x^s(t)$ are approximated by $\x_0^-(\tau)$ and $\x_0^+(\tau)$ respectively, where $$ \tau=t-\i\rho-\rho_1, $$ $\rho$ is defined in (\ref{Eq:rho}); and $\rho_1=\tfrac{3}{7}(\gamma-2)(\i\pi+\log6) $ takes into account the matching of the expansions (\ref{Eq:asimp0}) and (\ref{Eq:mainsing}). Comparing (\ref{Eq:approxtheta}), (\ref{Eq:tildetheta}) and (\ref{Eq:sgraph}) we obtain $$ A_1\approx 2|\Theta|\, |\e^{-2\pi\i\rho_1}| \, \e^{-2\pi\rho} =2|\Theta|\, \e^{-6\pi^2(\gamma-2)/7} \, \e^{-\sqrt2\pi^2/\root 4\of\mu}. $$ Now we calculate the width of the homoclinic zone: $$ \nu_+(\mu)-\nu_-(\mu) =\left.\frac{2 A_1(\mu,\nu)} { \frac{\partial A_0 }{\partial \nu} (\mu,\nu) }\right|_{\nu:A_0(\mu,\nu)=0}= \frac{ 5|\Theta|\e^{-6\pi^2(\gamma-2)/7} }{6 \mu^{5/4} } \, \e^{-\sqrt2\pi^2/\root 4\of\mu}, $$ where we used the approximations for $A_0$ and $A_1$. Thus we obtained the desired asymptotic (\ref{Eq:mainas}) for the width of the homoclinic zone on the parameter plane of the Bogdanov-Takens bifurcation for diffeomorphisms. The error term comes from the consideration of next order corrections to this asymptotic. \section{Numerical experiments\label{Se:numerics}} In the most cases there is not known ways to find the splitting constant $\Theta$ analyticly. Given a map $F_0$, this constant is not too difficult to compute with any reasonable precision. For the area-preserving H\'enon map this constant was computed with several thousands digits \cite{Simo2000}. We did high-precision computations of $\Theta$ for the family (\ref{Eq:nfl}) with $ f=x^2+\gamma xy $ for several $\gamma$. The method is essentially the same as in \cite{Gelfreich2000}. Numerically the splitting constant $\Theta$ does not vanish on the interval $[-0.5,2]$. Several values are given in the following table: \begin{center} \begin{tabular}{|l|l|} \hline $\gamma$&\hfil$\Theta$\hfil\\ \hline 0 & $5.202169191369226\cdot 10^{-5}$\\ 1 & $6.9898737i51682470943...$\\ 2 & $1.203229677075980622\cdot 10 ^{8}$\\ \hline \end{tabular} \end{center} The estimates for the width of the homoclinic zone were derived non-rigorously. So it is interesting to compare them with results of direct numerical computations. We choose the family (\ref{Eq:nfl}) with $$ f(x,y,\mu,\nu)=-\mu+x^2+\nu y+\gamma xy, $$ and the H\'enon map. There is a reasonably good agreement between our theory and experiments. For $\mu^{1/4}=0.08$ the relative error of the asymptotic formula is typically around 20\%. It is difficult to perform computations for essentially smaller values of $\mu$. So we took the data for several $\mu$ and then extrapolated towards $\mu=0$. The values of $\Theta$ obtained in this way coincide in several digits with the values from the table. This provides numerical evidence for the correctness of the asymptotic formula (\ref{Eq:mainas}). %% optional %\section{Summary} \section*{Acknowledgments} The author thanks the International Society for Analysis, Applications and Computation for presenting him the "ISAAC Award for Young Scientists". \begin{thebibliography}{12} \bibitem{Bogdanov1975} R.I. 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