%!PS-Adobe-2.0 %%Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %%Title: confol-fin.dvi %%Pages: 66 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: Times-Bold Times-Roman CMMI10 CMR7 CMR12 CMMI12 CMSY10 %%+ Times-Italic CMR8 MSBM10 CMMI8 CMSY8 CMEX10 MSAM10 CMR6 CMMI6 CMSY6 %%+ CMR10 TeX-cmex8 Courier %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips confol-fin.dvi %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2009.03.29:1945 %%BeginProcSet: tex.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc 0 0 % File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 % % @@psencodingfile@{ % author = "S. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: TeX-cmex8 %!PS-AdobeFont-1.0: TeX-cmex8 001.001 % Filtered by type1fix.pl 0.05 %%EndComments 13 dict dup begin /FontInfo 16 dict dup begin /Copyright (see\040copyright\040of\040original\040TeX\040font) def /FamilyName (TeX\040cmex8) def /FullName (TeX\040cmex8\040Regular) def /ItalicAngle 0 def /Notice (converted\040after\040April\0402001) def /UnderlinePosition -100 def /UnderlineThickness 50 def /Weight (Regular) def /isFixedPitch false def /version (001.001) def end readonly def /FontName /TeX-cmex8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 101 /e put readonly def /FontBBox {-29 -2957 1554 772} readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 6 /plusminus put dup 8 /circleplus put dup 15 /bullet put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 22 /precedesequal put dup 24 /similar put dup 26 /propersubset put dup 33 /arrowright put dup 39 /similarequal put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 59 /emptyset put dup 65 /A put dup 69 /E put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 90 /Z put dup 91 /union put dup 92 /intersection put dup 94 /logicaland put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 110 /backslash put readonly def /FontBBox{-29 -960 1116 775}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /prime put readonly def /FontBBox{-4 -948 1329 786}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 106 /j put dup 108 /l put dup 115 /s put readonly def /FontBBox{11 -250 1241 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put readonly def /FontBBox{-20 -250 1193 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /square put readonly def /FontBBox{8 -463 1331 1003}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 12 /vextendsingle put dup 26 /braceleftbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 82 /integraltext put dup 83 /uniontext put dup 91 /uniondisplay put dup 101 /tildewide put readonly def /FontBBox{-24 -2960 1454 772}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put dup 6 /plusminus put dup 48 /prime put dup 49 /infinity put dup 50 /element put readonly def /FontBBox{-30 -955 1185 779}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 13 /gamma put dup 17 /eta put dup 24 /xi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 33 /omega put dup 58 /period put dup 59 /comma put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 68 /D put dup 70 /F put dup 73 /I put dup 81 /Q put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 99 /c put dup 101 /e put dup 102 /f put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 6 /Sigma put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 61 /equal put readonly def /FontBBox{-36 -250 1070 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 13 /gamma put dup 14 /delta put dup 16 /zeta put dup 17 /eta put dup 21 /lambda put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 30 /phi put dup 31 /chi put dup 33 /omega put dup 34 /epsilon put dup 35 /theta1 put dup 39 /phi1 put dup 44 /arrowhookleft put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 110 /n put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-30 -250 1026 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 6 /Sigma put dup 10 /Omega put dup 23 /ring put dup 35 /numbersign put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 71 /G put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /circumflex put dup 99 /c put dup 101 /e put dup 102 /f put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 117 /u put dup 126 /tilde put readonly def /FontBBox{-34 -251 988 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%%Trailer %EOF %%EndDocument @endspecial 1638 3046 a(F)t Fy(I)t(G)t(U)t(R)t(E)34 b Fx(2)t(.)p Black 486 3237 a(Because)25 b Fv(F)39 b Fx(is)24 b(compact)h(and)g(the)f(singularities)f(of)i Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))24 b Fx(are)i(isolated)e(the)g (limit)386 3353 y(sets)30 b(of)h(indi)n(vidual)d(lea)n(v)o(es)i(of)g (the)h(characteristic)f(foliation)g(on)g Fv(F)44 b Fx(belong)30 b(to)g(one)386 3470 y(and)25 b(only)f(one)g(of)h(the)g(follo)n(wing)e (classes)h(\(cf.)32 b(Theorem)24 b(2.6.1.)30 b(of)25 b([24]\))p Black 602 3606 a Fu(\017)p Black 41 w Fx(\002x)o(ed)g (points,)p Black 602 3722 a Fu(\017)p Black 41 w Fx(closed)f(lea)n(v)o (es,)p Black 602 3839 a Fu(\017)p Black 41 w Fx(c)o(ycles)f(consisting) f(of)i(singular)e(points)g(and)i(lea)n(v)o(es)f(connecting)g(them)g (and)p Black 602 3955 a Fu(\017)p Black 41 w Fx(quasi-minimal)k(sets,)k (ie.)45 b(closures)29 b(of)h(non-periodic)e(recurrent)j(trajecto-)693 4071 y(ries.)386 4208 y(At)i(this)f(point)h(we)g(use)h(the)f 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5559 822 l gs col0 s gr % Polyline n 5321 1060 m 5248 1037 l 5271 1110 l gs col0 s gr % Polyline n 5898 486 m 5825 461 l 5852 533 l gs col0 s gr % Polyline n 6223 1377 m 6152 1352 l 6175 1423 l gs col0 s gr % Polyline n 5175 412 m 5248 436 l 5224 364 l gs col0 s gr % Polyline n 6068 738 m 6140 763 l 6115 690 l gs col0 s gr % Polyline n 5792 1037 m 5864 1060 l 5839 993 l gs col0 s gr % Polyline n 5476 1315 m 5547 1339 l 5525 1268 l gs col0 s gr % Polyline 2 slj n 5501 425 m 5355 282 l gs col0 s gr % Polyline n 5212 715 m 5092 594 l gs col0 s gr % Polyline 0 slj n 762 1872 m 1967 1872 l 1967 3074 l 762 3074 l cp gs col0 s gr % Polyline n 1967 1872 m 762 3074 l gs col0 s gr % Polyline n 1363 1872 m 762 2473 l gs col0 s gr % Polyline n 1967 2473 m 1363 3074 l gs col0 s gr % Polyline n 1715 2774 m 1641 2798 l 1666 2725 l gs col0 s gr % Polyline n 1390 2497 m 1316 2521 l 1339 2450 l gs col0 s gr % Polyline n 1134 2149 m 1063 2174 l 1086 2102 l gs col0 s gr % Polyline 2 slj n 1908 1872 m 1906 1873 l 1903 1876 l 1897 1882 l 1888 1889 l 1877 1899 l 1864 1910 l 1849 1923 l 1833 1937 l 1815 1952 l 1797 1967 l 1777 1984 l 1755 2002 l 1731 2021 l 1705 2042 l 1677 2064 l 1650 2085 l 1626 2104 l 1606 2119 l 1592 2131 l 1582 2139 l 1576 2145 l 1572 2149 l 1570 2153 l 1567 2156 l 1563 2159 l 1557 2164 l 1547 2171 l 1533 2181 l 1513 2193 l 1489 2206 l 1461 2221 l 1429 2236 l 1401 2248 l 1378 2257 l 1362 2262 l 1350 2265 l 1342 2267 l 1336 2267 l 1330 2267 l 1322 2268 l 1311 2270 l 1296 2273 l 1275 2278 l 1249 2285 l 1221 2293 l 1190 2301 l 1166 2307 l 1150 2311 l 1141 2312 l 1137 2312 l 1136 2311 l 1135 2310 l 1132 2309 l 1124 2311 l 1110 2314 l 1089 2321 l 1063 2330 l 1037 2340 l 1014 2349 l 998 2356 l 988 2361 l 981 2363 l 976 2366 l 972 2368 l 965 2371 l 955 2377 l 940 2386 l 919 2398 l 894 2413 l 870 2429 l 849 2444 l 831 2457 l 816 2470 l 803 2481 l 792 2492 l 782 2501 l 773 2509 l 767 2515 l 764 2519 l 762 2521 l gs col0 s gr % Polyline n 762 2413 m 763 2412 l 764 2411 l 767 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1945 2763 l 1949 2761 l 1952 2760 l 1955 2759 l 1958 2759 l 1960 2758 l 1962 2758 l 1963 2758 l 1964 2757 l 1965 2757 l 1966 2758 l 1967 2758 l 1967 2759 l 1968 2759 l 1968 2760 l 1967 2760 l 1967 2761 l gs col0 s gr % Polyline n 1967 1942 m 1966 1943 l 1962 1945 l 1957 1948 l 1950 1952 l 1942 1958 l 1932 1966 l 1920 1975 l 1906 1988 l 1890 2004 l 1870 2025 l 1847 2051 l 1829 2073 l 1812 2093 l 1797 2111 l 1786 2125 l 1777 2136 l 1769 2144 l 1764 2151 l 1759 2156 l 1754 2162 l 1749 2168 l 1742 2178 l 1733 2190 l 1722 2206 l 1708 2228 l 1693 2253 l 1677 2281 l 1660 2313 l 1647 2340 l 1637 2361 l 1631 2375 l 1628 2384 l 1627 2390 l 1627 2393 l 1627 2397 l 1626 2402 l 1624 2411 l 1620 2426 l 1613 2448 l 1604 2476 l 1594 2509 l 1585 2539 l 1578 2565 l 1572 2588 l 1568 2605 l 1565 2618 l 1563 2628 l 1563 2635 l 1563 2641 l 1562 2647 l 1562 2653 l 1560 2662 l 1557 2675 l 1553 2691 l 1547 2711 l 1540 2735 l 1531 2761 l 1519 2793 l 1509 2817 l 1503 2834 l 1499 2843 l 1497 2847 l 1496 2848 l 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1881 l 3413 3084 l 2208 3084 l cp gs col0 s gr % Polyline n 3413 1881 m 2208 3084 l gs col0 s gr % Polyline n 2849 2494 m 2773 2519 l 2800 2446 l gs col0 s gr % Polyline 2 slj n 2207 1360 m 2210 1357 l 2216 1350 l 2227 1338 l 2242 1321 l 2259 1302 l 2279 1280 l 2299 1258 l 2318 1236 l 2336 1216 l 2352 1197 l 2367 1180 l 2382 1164 l 2395 1149 l 2408 1134 l 2421 1119 l 2432 1105 l 2444 1091 l 2456 1077 l 2469 1062 l 2481 1046 l 2494 1030 l 2508 1014 l 2521 997 l 2534 980 l 2547 963 l 2560 946 l 2572 930 l 2584 914 l 2595 898 l 2606 883 l 2616 868 l 2626 854 l 2635 840 l 2645 824 l 2654 808 l 2663 792 l 2672 776 l 2681 759 l 2689 742 l 2697 724 l 2705 707 l 2712 689 l 2719 671 l 2726 654 l 2731 637 l 2736 620 l 2741 604 l 2746 588 l 2750 572 l 2753 556 l 2757 539 l 2760 521 l 2763 502 l 2766 481 l 2770 457 l 2773 432 l 2776 404 l 2780 375 l 2783 347 l 2786 320 l 2788 299 l 2790 283 l 2791 273 l 2791 270 l 2791 269 l gs col0 s gr % Polyline n 2784 1471 m 2784 1470 l 2784 1467 l 2785 1459 l 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%%Trailer %EOF %%EndDocument @endspecial 1611 2242 a Fx(F)t Fy(I)t(G)t(U)t(R)t(E)33 b Fx(1)t(2)t(.)p Black 386 2438 a(tangent)g(to)f Fv(@)874 2453 y Fo(t)938 2438 y Fx(on)h(a)g(neighbourhood)f(of)h(the)g(boundary) g(\(cf.)56 b([15]\).)h(Then)33 b(there)386 2554 y(are)27 b(smooth)f(functions)f Fv(f)1300 2569 y Fo(i)1329 2554 y Fv(;)17 b(g)1420 2569 y Fo(i)1447 2554 y Fv(;)g(i)31 b Fu(2)h(f)p Fw(0)p Fv(;)17 b Fw(1)p Fu(g)26 b Fx(on)g(this)g (neighbourhood)f(such)i(that)f Fv(\030)31 b Fx(is)386 2670 y(spanned)24 b(by)h Fv(@)913 2685 y Fo(t)968 2670 y Fx(and)1217 2919 y Fv(f)1265 2934 y Fs(0)1305 2919 y Fw(\()p Fv(t)p Fw(\))p Fv(@)1467 2934 y Fs(1)1529 2919 y Fw(+)d Fv(g)1674 2934 y Fs(0)1713 2919 y Fw(\()p Fv(t)p Fw(\))p Fv(@)1875 2934 y Fs(2)1940 2919 y Fx(near)j Fv(T)2207 2878 y Fs(2)2268 2919 y Fu(\002)e(f)p Fw(0)p Fu(g)1217 3080 y Fv(f)1265 3095 y Fs(1)1305 3080 y Fw(\()p Fv(t)p Fw(\))p Fv(@)1467 3095 y Fs(1)1529 3080 y Fw(+)f Fv(g)1674 3095 y Fs(1)1713 3080 y Fw(\()p Fv(t)p Fw(\))p Fv(@)1875 3095 y Fs(2)1940 3080 y Fx(near)j Fv(T)2207 3038 y Fs(2)2268 3080 y Fu(\002)e(f)p Fw(1)p Fu(g)p Fv(:)386 3002 y Fx(\(4\))386 3237 y(Because)30 b Fv(\030)j Fx(is)28 b(a)h(positi)n(v)o(e)d(contact)j (structure,)g(the)f(functions)g Fv(f)2649 3252 y Fo(i)2677 3237 y Fv(;)17 b(g)2768 3252 y Fo(i)2825 3237 y Fx(satisfy)28 b(the)g(in-)386 3353 y(equalities)38 b Fv(f)866 3317 y Fn(0)855 3378 y Fo(i)889 3353 y Fw(\()p Fv(t)p Fw(\))p Fv(g)1047 3368 y Fo(i)1075 3353 y Fw(\()p Fv(t)p Fw(\))32 b Fu(\000)h Fv(g)1379 3317 y Fn(0)1375 3378 y Fo(i)1403 3353 y Fw(\()p Fv(t)p Fw(\))p Fv(f)1562 3368 y Fo(i)1591 3353 y Fw(\()p Fv(t)p Fw(\))53 b Fv(>)h Fw(0)39 b Fx(for)g Fv(i)54 b Fu(2)g(f)p Fw(0)p Fv(;)17 b Fw(1)p Fu(g)38 b Fx(on)g(their)h(respecti)n(v)o(e)386 3469 y(domains.)486 3585 y(W)-8 b(e)23 b(no)n(w)f(modify)g Fv(\030)28 b Fx(to)23 b(a)g(confoliation)1896 3559 y Fw(~)1886 3585 y Fv(\030)28 b Fx(on)23 b Fv(V)49 b Fw(=)27 b Fv(T)2360 3549 y Fs(2)2416 3585 y Fu(\002)16 b Fw([0)p Fv(;)h 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Fw(~)-52 b Fv(g)2207 4059 y Fn(0)2203 4120 y Fo(i)2230 4096 y Fw(\()p Fv(t)p Fw(\))2363 4069 y(~)2341 4096 y Fv(f)2389 4111 y Fo(i)2418 4096 y Fw(\()p Fv(t)p Fw(\))29 b Fv(>)f Fw(0)e Fx(if)f Fv(t)k Fu(2)g Fw(\()p Fv(\034)6 b(;)17 b Fw(1)22 b Fu(\000)h Fv(\034)11 b Fw(\))693 4212 y Fx(and)p Black 602 4328 a Fu(\017)p Black 714 4302 a Fw(~)693 4328 y Fv(f)752 4292 y Fn(0)741 4353 y Fo(i)775 4328 y Fw(\()p Fv(t)p Fw(\))s(~)-52 b Fv(g)933 4343 y Fo(i)961 4328 y Fw(\()p Fv(t)p Fw(\))22 b Fu(\000)k Fw(~)-52 b Fv(g)1245 4292 y Fn(0)1241 4353 y Fo(i)1269 4328 y Fw(\()p Fv(t)p Fw(\))1401 4302 y(~)1380 4328 y Fv(f)1428 4343 y Fo(i)1456 4328 y Fw(\()p Fv(t)p Fw(\))28 b Fu(\021)g Fw(0)d Fx(for)g Fv(t)j Fu(2)g Fw([0)p Fv(;)17 b(\034)11 b Fw(])22 b Fu([)h Fw([1)f Fu(\000)g Fv(\034)6 b(;)17 b Fw(1])p Black 602 4454 a Fu(\017)p Black 714 4427 a Fw(~)693 4454 y Fv(f)741 4469 y Fo(i)769 4454 y Fv(;)j Fw(~)-52 b Fv(g)860 4469 y Fo(i)913 4454 y Fx(coincide)24 b(with)g Fv(f)1525 4469 y Fo(i)1554 4454 y Fv(;)17 b(g)1645 4469 y Fo(i)1697 4454 y Fx(at)25 b Fv(t)j Fw(=)f(0)p Fv(;)17 b Fw(1)p Fx(.)p Black 386 4621 a FD(Remark)38 b(4.1.)p Black 49 w Fx(From)f(the)h(proof)g(of)g(Theorem)f(1.5)h(in)f ([16])h(it)f(follo)n(ws)g(that)g(the)386 4743 y(contact)25 b(structure)1082 4717 y Fw(~)1072 4743 y Fv(\030)k Fx(on)c Fv(T)1340 4707 y Fs(2)1401 4743 y Fu(\002)e Fw(\()p Fv(\034)6 b(;)17 b Fw(1)k Fu(\000)i Fv(\034)11 b Fw(\))25 b Fx(is)g(tight.)486 4910 y(W)-8 b(e)21 b(write)g Fv(\030)k Fx(for)d(the)e(confoliation)g (constructed)g(so)h(f)o(ar)-5 b(.)30 b(In)21 b(the)g(ne)o(xt)f(step)g (we)i(will)386 5026 y(e)o(xtend)30 b Fv(\030)35 b Fx(to)30 b(a)h(smooth)e(confoliation)g(on)h Fv(T)1979 4990 y Fs(2)2045 5026 y Fu(\002)d Fw([)p Fu(\000)p Fw(1)p Fv(;)17 b Fw(2])31 b Fx(such)f(that)g(the)g(boundary)386 5142 y(consists)23 b(of)i(torus)f(lea)n(v)o(es.)486 5259 y(Let)30 b Fv(h)g Fx(be)h(a)f(dif)n(feomorphism)e(of)j Fp(R)1790 5217 y Fs(+)1790 5283 y(0)1879 5259 y Fx(such)f(that)g Fv(h)p Fw(\()p Fv(s)p 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l 996 2616 l 981 2607 l 965 2596 l 946 2583 l 926 2568 l 906 2553 l 890 2542 l 879 2534 l 873 2530 l 870 2528 l 869 2528 l 868 2527 l 865 2525 l 858 2519 l 846 2509 l 828 2493 l 805 2472 l 784 2452 l 766 2435 l 750 2421 l 739 2411 l 731 2404 l 725 2400 l 720 2397 l 716 2394 l 710 2389 l 701 2381 l 690 2368 l 674 2350 l 655 2325 l 634 2296 l 616 2269 l 600 2245 l 587 2224 l 578 2208 l 571 2197 l 567 2188 l 564 2183 l 562 2178 l 560 2173 l 557 2167 l 553 2158 l 548 2145 l 540 2128 l 530 2104 l 517 2076 l 504 2044 l 491 2012 l 480 1983 l 472 1960 l 466 1942 l 462 1930 l 459 1922 l 458 1916 l 457 1913 l 457 1909 l 456 1903 l 454 1895 l 451 1882 l 445 1863 l 438 1839 l 430 1808 l 420 1773 l 410 1738 l 402 1706 l 395 1680 l 389 1660 l 386 1645 l 383 1635 l 381 1628 l 380 1623 l 378 1617 l 377 1610 l 374 1600 l 371 1586 l 366 1565 l 360 1539 l 353 1507 l 345 1471 l 338 1436 l 331 1404 l 326 1379 l 322 1361 l 320 1349 l 319 1341 l 318 1336 l 317 1334 l 317 1331 l 316 1326 l 315 1318 l 313 1306 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begin 32 31 bop Black 386 244 a Fq(32)1256 b(T)-6 b(.)19 b(V)m(OGEL)p Black 486 455 a Fx(W)-8 b(e)25 b(no)n(w)g(sho)n(w)f (\(i\).)33 b(Let)25 b Fv(x)k Fu(2)g Fv(\013)q Fw(\(\000\))c Fx(be)h(an)f(elliptic)f(singularity)g(such)h(that)p 3159 368 216 4 v 25 w Fv(\013)q Fw(\()p Fv(Q)p Fw(\))386 571 y Fx(is)32 b(not)g(a)h(neighbourhood)d(of)j Fv(x)p Fx(.)54 b(Then)32 b(the)h(connected)f(component)g(of)g Fv(@)5 b Fw(\()p Fv(\013)q Fw(\()p Fv(Q)p Fw(\)\))386 687 y Fx(containing)27 b Fv(x)i Fx(is)e(a)i(piece)n(wise)f(smooth)e(closed)i (curv)o(e)g Fv(c)p Fx(.)41 b(After)29 b(a)f(perturbation)g(of)386 804 y(the)d(sphere)h(we)g(may)f(assume)h(that)f Fv(c)g Fx(does)h(not)f(contain)g(corners,)h Fv(x)k Fu(2)g Fv(H)8 b Fw(\()p Fv(\030)d Fw(\))24 b Fx(and)i Fv(c)386 920 y Fx(is)e(embedded)f(\(cf.)31 b(Figure)25 b(10\).)30 b(If)24 b(all)g(singularities)e(on)i Fv(c)g Fx(were)h(ne)o(gati)n(v)o (e,)d(then)i(we)386 1036 y(w)o(ould)f(get)h(a)h(contradiction)e(to)h (the)g(tightness)f(of)h Fv(\030)29 b Fx(since)24 b(no)g(inte)o(gral)f (surf)o(ace)i(of)f Fv(\030)386 1152 y Fx(can)j(meet)g Fv(x)p Fx(.)37 b(Since)27 b(all)f(elliptic)g(singularities)f(on)h Fv(c)31 b Fu(\032)h Fv(\013)q Fw(\()p Fv(@)5 b(Q)p Fw(\))28 b Fx(are)f(attracti)n(v)o(e)f(and)386 1269 y(therefore)f(ne)o(gati)n(v) o(e,)e(there)i(must)e(be)i(a)h(positi)n(v)o(e)c(pseudo)o(v)o(erte)o(x)h (on)h Fv(c)p Fx(.)486 1385 y(It)j(remains)h(to)f(pro)o(v)o(e)g(\(ii\).) 39 b(Assume)27 b Fv(d)1861 1400 y Fs(+)1920 1385 y Fw(\()p Fv(U)10 b Fw(\))33 b(=)h(1)27 b Fx(and)h(let)f Fv(x)2645 1400 y Fs(1)2685 1385 y Fv(;)17 b(:)g(:)g(:)f(;)h(x)2959 1400 y Fo(l)2985 1385 y Fv(;)g(l)35 b Fu(\025)f Fw(2)28 b Fx(be)386 1501 y(the)d(pseudo)o(v)o(ertices)e(separating)h(the)h (edges)f Fv(e)2024 1516 y Fo(i)2053 1501 y Fv(;)17 b(e)2142 1465 y Fn(0)2142 1526 y Fo(i)2170 1501 y Fv(;)g(i)27 b Fw(=)h(1)p Fv(;)17 b(:)g(:)g(:)f(;)h(l)r Fx(.)486 1617 y(When)31 b Fv(\013)q Fw(\()p Fv(e)901 1581 y Fn(0)901 1642 y Fo(i)929 1617 y Fw(\))41 b(=)g Fv(\013)q 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Fo(j)2573 1970 y Fw(\))32 b Fx(be)g(tw)o(o)f(hyperbolic)386 2087 y(singularities)26 b(which)h(lie)h(on)g(the)g(c)o(ycle)f(associated)h(to)f(identi\002ed)h (edges)g(\(cf.)40 b(Def-)386 2203 y(inition)26 b(3.3\))i(and)g(are)h (connected)f(by)g(a)g(piece)n(wise)g(smooth)f(simple)f(oriented)i(path) 386 2319 y Fv(\033)j Fx(in)c(the)g(complement)f(of)h Fv(U)38 b Fx(consisting)26 b(of)h(lea)n(v)o(es)g(of)g Fv(S)6 b Fw(\()p Fv(\030)f Fw(\))26 b Fx(and)h(hyperbolic)f(sin-)386 2435 y(gularities)f(\(as)i(corners\))g(such)g(that)f Fv(\033)k Fx(starts)c(at)h Fv(\013)q Fw(\()p Fv(x)2242 2450 y Fo(i)2270 2435 y Fw(\))g Fx(and)f(ends)g(at)h Fv(\013)q Fw(\()p Fv(x)2969 2450 y Fo(j)3006 2435 y Fw(\))f Fx(without)386 2551 y(passing)e(through)h(images)g(of)h(other)f(pseudo) o(v)o(ertices.)31 b(After)26 b(a)g(small)f(perturbation)386 2668 y(of)j Fv(S)33 b Fx(in)27 b(the)h(neighbourhood)e(of)i Fv(\013)q Fw(\()p Fv(x)1743 2683 y Fo(j)1779 2668 y Fw(\))g Fx(we)g(obtain)e(a)i(sphere)g Fv(S)2691 2632 y 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Black 486 1893 a(Note)26 b(that)g(if)g Fv(\015)31 b Fx(has)26 b(non-tri)n(vial)f(in\002nitesimal)g(\(or)h (only)g(attracti)n(v)o(e\))f(holonomy)-6 b(,)386 2010 y(then)36 b(the)h(statement)f(of)h(Lemma)f(6.3)g(can)h(be)g(sharpened)g (in)f(the)h(sense)g(that)f(the)386 2126 y(lemma)28 b(remains)h(true)g (for)g Fv(C)1437 2090 y Fn(1)1512 2126 y Fx(-neighbourhoods)e(of)i Fv(\030)34 b Fx(because)c(the)f(function)f Fv(g)39 b Fw(:)386 2242 y([)p Fu(\000)p Fw(1)p Fv(;)17 b Fw(1])28 b Fu(\000)-17 b(!)28 b Fw([)p Fu(\000)p Fw(1)p Fv(;)17 b Fw(1])j Fx(can)i(be)e(chosen)h Fv(C)1817 2206 y Fn(1)1891 2242 y Fx(-close)g(to)f(the)h(identity)-6 b(.)27 b(In)21 b(the)g(follo)n(wing)386 2358 y(we)38 b(will)f(consider)g(only)g Fv(C)1400 2322 y Fs(0)1439 2358 y Fx(-approximations.)68 b(This)37 b(allo)n(ws)f(us)h(to)h(choose)f(the)386 2475 y(approximation)31 b(of)i Fv(\030)k Fx(more)32 b(freely)-6 b(.)55 b(In)33 b(particular)f(we)h(can)g(preserv)o(e)g(qualitati)n(v)o (e)386 2591 y(features)25 b(of)g(the)g(characteristic)g(foliation)e(on) i(surf)o(aces)g(transv)o(erse)f(to)h Fv(\015)5 b Fx(.)p Black 386 2786 a FD(Lemma)36 b(6.4.)p Black 47 w Ft(Let)g Fv(\030)41 b Ft(be)35 b(a)h Fv(C)1484 2750 y Fo(k)1527 2786 y Ft(-confoliation,)g Fv(k)51 b Fu(\025)d Fw(1)p Ft(,)38 b(and)e Fv(\015)k Ft(a)c(simple)f(Le)l(g)o(en-)386 2902 y(drian)25 b(se)l(gment)h(suc)o(h)f(that)g(both)g(endpoints)g(of)h Fv(\015)31 b Ft(lie)26 b(in)f(the)h(contact)g(r)l(e)l(gion)f(and)h Fv(\015)386 3018 y Ft(inter)o(sects)e Fv(F)38 b Ft(tr)o(ansver)o(sely) 24 b(and)g(at)g(most)h(once)o(.)486 3135 y(Then)31 b(e)o(very)h Fv(C)1039 3098 y Fo(k)1081 3135 y Ft(-neighbourhood)e(of)g Fv(\030)36 b Ft(contains)30 b(a)h(confoliation)e Fv(\030)2953 3098 y Fn(0)3007 3135 y Ft(suc)o(h)i(that)386 3251 y Fv(\030)434 3215 y Fn(0)507 3251 y Fw(=)49 b Fv(\030)42 b Ft(outside)35 b(a)i(neighbourhood)e(of)h Fv(\015)42 b Ft(and)36 b Fv(\030)2215 3215 y Fn(0)2275 3251 y Ft(is)g(a)h(contact) f(structur)l(e)g(on)h(a)386 3367 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3349 y Fx(in)24 b(the)h(proof)g(of)g (Lemma)f(6.3,)g(cf.)31 b(also)25 b(Lemma)f(2.5.2)g(in)h([9].)486 3465 y(Fix)i(a)h(neighbourhood)e Fv(U)44 b Fu(')34 b Fv(S)1636 3429 y Fs(1)1630 3490 y Fo(x)1699 3465 y Fu(\002)25 b Fw([)p Fu(\000)p Fw(1)p Fv(;)17 b Fw(1])2074 3480 y Fo(y)2140 3465 y Fu(\002)24 b Fw([)p Fu(\000)p Fw(1)p Fv(;)17 b Fw(1])2514 3480 y Fo(z)2582 3465 y Fx(such)27 b(that)h Fv(\015)38 b Fw(=)33 b Fv(S)3234 3429 y Fs(1)3297 3465 y Fu(\002)386 3582 y(f)p Fw(\(0)p Fv(;)17 b Fw(0\))p Fu(g)27 b Fx(and)h(the)g(coordinates)g Fv(x;)17 b(y)t(;)g(z)32 b Fx(ha)n(v)o(e)c(all)g(properties)g(used)g(in)f(the)i(proof)f(of)386 3698 y(Lemma)h(6.3.)44 b(In)30 b(particular)l(,)g(the)g(foliation)e(by) h(the)g(second)h(f)o(actor)f(is)h(Le)o(gendrian)386 3814 y(and)24 b(coincides)f(with)g Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))24 b Fx(on)f Fv(F)33 b Fu(\\)20 b Fv(U)34 b Fx(while)24 b(the)g(third)f(f)o(actor)h(is)g(positi)n(v)o(ely)d(trans-)386 3930 y(v)o(erse)i(to)h Fv(\030)5 b Fx(.)29 b(W)-8 b(e)25 b(require)e(that)h Fv(U)34 b Fx(intersects)23 b Fv(F)38 b Fx(only)22 b(in)i(neighbourhoods)d(of)j(points)386 4047 y(in)g Fv(\015)j Fu(\\)c Fw(\012)725 4062 y Fo(Q)813 4047 y Fw(=:)k Fv(X)8 b Fx(.)486 4163 y(Let)26 b(us)f(mak)o(e)i(an)f (orientation)f(assumption)f(in)i(order)g(to)g(simplify)f(the)h (presenta-)386 4279 y(tion:)45 b(W)-8 b(e)33 b(assume)g(that)f(the)g (orientation)g(of)h(the)f(Le)o(gendrian)g(foliation)g(on)g Fv(S)3230 4243 y Fs(1)3297 4279 y Fu(\002)386 4395 y Fw([)p Fu(\000)p Fw(1)p Fv(;)17 b Fw(1])25 b Fu(\002)h Fw([)p Fu(\000)p Fw(1)p Fv(;)17 b Fw(1])29 b Fx(gi)n(v)o(en)e(by)i(the) g(second)f(f)o(actor)i(coincides)e(with)g(the)h(orientation)386 4511 y(of)h Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))28 b Fx(near)i(points)e(of)i Fv(\015)h Fu(\\)26 b Fv(\015)1540 4526 y Fo(v)1580 4511 y Fv(;)17 b(v)40 b Fu(2)d Fv(V)21 b Fx(,)31 b(ie.)45 b(in)29 b(Figure)h(20)f(the)h(foliation)e(is)h(ori-) 386 4628 y(ented)37 b(from)f(left)h(to)f(right.)67 b(When)36 b(this)g(assumption)f(is)i(not)f(satis\002ed)g(for)h(some)386 4744 y Fv(y)44 b Fu(2)e Fv(\015)33 b Fu(\\)28 b Fw(\012)834 4759 y Fo(Q)894 4744 y Fx(,)34 b(then)e(one)g(has)g(to)g(interchange)g (the)g(roles)f(of)38 b Fw(^)-54 b Fv(\034)2642 4759 y Fn(\000)2701 4744 y Fw(\()p Fv(y)t Fw(\))31 b Fx(and)38 b Fw(^)-54 b Fv(\034)3079 4759 y Fs(+)3138 4744 y Fw(\()p Fv(y)t Fw(\))31 b Fx(in)386 4860 y(some)24 b(of)h(the)g(follo)n(wing)e (ar)n(guments.)486 4976 y(By)36 b(transv)o(ersality)f Fv(\015)42 b Fx(intersects)36 b Fv(F)50 b Fx(in)36 b(a)h(\002nite)g (number)f(of)g(points.)65 b(Since)37 b Fv(\015)386 5093 y Fx(is)d(contained)g(in)g(the)h(fully)f(foliated)g(part)g(of)h Fv(\030)5 b Fx(,)36 b Fv(\015)k Fx(cannot)34 b(intersect)g Fv(\013)q Fw(\()p Fv(Q)p Fw(\))h Fx(since)386 5209 y(e)n(v)o(ery)g (point)g(of)h Fv(\013)q Fw(\()p Fv(Q)p Fw(\))g Fx(is)g(connected)g(to)f Fv(H)8 b Fw(\()p Fv(\030)d Fw(\))35 b Fx(by)h(a)g(Le)o(gendrian)f(arc.) 65 b(W)-8 b(e)36 b(can)386 5337 y(ignore)26 b(the)g(points)g(in)g Fv(F)37 b Fu(\\)24 b Fv(\015)31 b Fx(which)26 b(do)g(not)g(belong)g(to) p 2414 5250 216 4 v 26 w Fv(\013)q Fw(\()p Fv(Q)p Fw(\))h Fx(if)f(we)h(deform)f Fv(\030)31 b Fx(on)386 5453 y(a)25 b(neighbourhood)e(of)i Fv(\015)30 b Fx(which)24 b(is)h(small)f(enough.) p Black Black eop end %%Page: 58 58 TeXDict begin 58 57 bop Black 386 244 a Fq(58)1256 b(T)-6 b(.)19 b(V)m(OGEL)p Black 486 443 a Fx(Because)34 b Fv(F)46 b Fx(is)33 b(smoothly)e(embedded)h(and)h Fv(\030)k Fx(is)c Fv(C)2340 407 y Fs(2)2379 443 y Fx(-smooth,)h Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))32 b Fx(is)g(also)h(of)386 560 y(class)d Fv(C)687 523 y Fs(2)727 560 y Fx(.)48 b(As)31 b(we)g(ha)n(v)o(e)f(already)h(mentioned)e(in)i(Section)f(3.2)h(the)f Fv(!)t Fx(-limit)f(set)h Fv(\015)3334 575 y Fo(v)386 676 y Fx(with)k Fv(v)49 b Fu(2)d Fv(V)56 b Fx(is)35 b(either)f(a)h (quasi-minimal)d(set)j(or)f(we)h(may)f(assume)g(that)g Fv(\015)3154 691 y Fo(v)3229 676 y Fx(is)g(a)386 792 y(closed)24 b(leaf)i(of)f Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))p Fx(.)29 b(W)-8 b(e)26 b(distinguish)c(the)i(follo)n(wing)f (cases.)p Black 558 933 a(\(i\))p Black 41 w Fv(\015)744 948 y Fo(v)806 933 y Fx(is)d(quasi-minimal.)28 b(Since)21 b(there)h(are)g(interior)e(points)g(of)h Fv(\013)q Fw(\()p Fv(Q)p Fw(\))g Fx(arbitrar)n(-)693 1049 y(ily)31 b(close)h(to)f Fv(\015)1227 1064 y Fo(v)1268 1049 y Fx(,)i(there)f(is)g(no)f(se)o (gment)g Fv(\034)43 b Fx(transv)o(erse)31 b(to)h Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))31 b Fx(such)g(that)693 1166 y Fv(\034)24 b Fu(\\)12 b Fv(\015)888 1181 y Fo(v)951 1166 y Fx(is)22 b(dense)g(in)g Fv(\034)11 b Fx(.)30 b(Then)22 b Fv(\015)1775 1181 y Fo(v)1828 1166 y Fu(\\)12 b Fv(\034)35 b Fx(is)21 b(a)i(Cantor)f(set)g(\(cf.)31 b([17)o(]\).)g(The)22 b(inter)n(-)693 1282 y(section)31 b(between)g(tw)o(o)g(dif)n(ferent)f (quasi-minimal)f(sets)i(cannot)g(contain)f(a)693 1398 y(recurrent)d(orbit)g(by)f(Maier')-5 b(s)26 b(theorem)h(\(Theorem)g (2.4.1)f(in)g([24]\))h(and)g(the)693 1514 y(number)j(of)h (quasi-minimal)e(sets)h(of)h Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))30 b Fx(is)g(bounded)g(by)h(the)f(genus)h(of)693 1631 y Fv(F)39 b Fx(according)24 b(to)h(Theorem)f(2.4.5.)30 b(in)25 b([24].)p Black 530 1747 a(\(ii\))p Black 41 w Fv(\015)744 1762 y Fo(v)809 1747 y Fx(is)f(a)h(closed)f(leaf)h(of)f Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))24 b Fx(whose)g(holonomy)f(is)h (attracti)n(v)o(e)f(on)h(the)g(side)693 1863 y(from)38 b(which)f Fv(\013)q Fw(\()p Fv(Q)p Fw(\))h Fx(accumulates)g(on)g Fv(\015)2180 1878 y Fo(v)2258 1863 y Fx(while)g(it)f(is)h(repulsi)n(v)o (e)e(on)i(the)693 1979 y(other)33 b(side)h(and)f Fv(\013)q Fw(\()p Fv(Q)p Fw(\))h Fx(spirals)e(onto)h Fv(\015)2108 1994 y Fo(v)2182 1979 y Fx(on)h(the)f(attracti)n(v)o(e)g(side.)56 b(In)34 b(this)693 2096 y(case,)41 b Fv(\013)q Fw(\()p Fv(Q)p Fw(\))36 b Fx(cannot)h(enter)g(a)h(one-sided)e(neighbourhood)g (of)h Fv(\015)3039 2111 y Fo(v)3116 2096 y Fx(on)g(the)693 2212 y(side)24 b(where)i(the)e(holonomy)f(is)i(repulsi)n(v)o(e.)p Black 502 2328 a(\(iii\))p Black 41 w Fv(\015)744 2343 y Fo(v)807 2328 y Fx(is)e(a)g(closed)f(leaf)h(of)g Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))22 b Fx(whose)g(holonomy)f(is)i(attracti)n (v)o(e)e(on)i(one)f(side)693 2444 y(and)k(either)h(there)f(is)g(a)h (sequence)f(of)h(closed)f(lea)n(v)o(es)g(of)g Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))26 b Fx(on)g(the)g(other)693 2560 y(side)33 b(of)g Fv(\015)1054 2575 y Fo(v)1128 2560 y Fx(which)f(con)l(v)o(er)n(ge)h(to)g Fv(\015)1957 2575 y Fo(v)2031 2560 y Fx(or)g Fv(\015)2198 2575 y Fo(v)2272 2560 y Fx(has)g(attracti)n(v)o(e)f(holonomy)f(on)693 2677 y(both)24 b(sides.)486 2818 y(If)33 b Fv(\015)636 2833 y Fo(v)710 2818 y Fx(belongs)f(to)h(class)g(\(iii\))f(and)h Fv(U)44 b Fx(is)33 b(small)f(enough)h(\(ie.)56 b(contained)32 b(in)h(the)386 2934 y(interior)27 b(of)h(an)h(annulus)e(each)h(of)g (whose)g(boundary)f(is)h(tangent)f(to)h Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))27 b Fx(or)h(trans-)386 3050 y(v)o(erse)i(to)g Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))29 b Fx(such)h(that)f Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))30 b Fx(points)e(into)i(the)g (annulus)f(along)g(the)h(boundary\),)386 3166 y(then)21 b(an)o(y)g(modi\002cation)f(of)h Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))20 b Fx(with)h(support)f(in)h Fv(U)f Fu(\\)9 b Fv(F)35 b Fx(will)21 b(result)f(in)h(a)h(singular)386 3283 y(foliation)g(on)h Fv(F)37 b Fx(such)23 b(that)g(all)g(lea)n(v)o (es)g(of)h(the)f(characteristic)h(foliation)e(which)h(enter)386 3399 y(a)h(neighbourhood)e(of)i Fv(\015)1239 3414 y Fo(v)1304 3399 y Fx(containing)e Fv(U)35 b Fx(will)23 b(remain)h(in)f Fv(U)35 b Fx(fore)n(v)o(er)23 b(e)n(v)o(en)g(after)i(the)386 3515 y(modi\002cation.)63 b(When)35 b(no)h(singularities)e(are)j (created)f(during)f(the)h(modi\002cation,)386 3631 y(then)27 b(the)h(modi\002cation)e(replaces)i Fw(\()p Fv(Q;)17 b(V)5 b(;)17 b(\013)q Fw(\))27 b Fx(by)g(an)h(o)o(v)o(ertwisted)e(star) h Fw(\()p Fv(Q)3038 3595 y Fn(0)3062 3631 y Fv(;)17 b(V)3184 3595 y Fn(0)3207 3631 y Fv(;)g(\013)3314 3595 y Fn(0)3337 3631 y Fw(\))386 3748 y Fx(such)29 b(that)g Fu(j)p Fv(V)21 b Fu(j)36 b Fw(=)f Fu(j)p Fv(V)1165 3711 y Fn(0)1188 3748 y Fu(j)p Fx(.)44 b(In)29 b(this)f(case)i Fv(\015)1822 3763 y Fo(v)1899 3748 y Fu(6)p Fw(=)36 b Fv(\015)2067 3711 y Fn(0)2062 3772 y Fo(v)2131 3748 y Fx(b)n(ut)29 b Fv(\015)2342 3711 y Fn(0)2337 3772 y Fo(v)2407 3748 y Fx(is)g(a)g(closed)g(leaf)h(of)f Fv(F)14 b Fw(\()p Fv(\030)3314 3711 y Fn(0)3337 3748 y Fw(\))386 3864 y Fx(which)22 b(passes)h(through)f Fv(H)8 b Fw(\()p Fv(\030)1438 3828 y Fn(0)1460 3864 y Fw(\))23 b Fx(\(by)g(the)f(proof)h(of)g(Lemma)f (6.3.)30 b(W)-8 b(e)23 b(k)o(eep)g(this)f(case)386 3980 y(separated)f(from)g(the)f(others)h(although)e(all)i(three)g(of)g(them) f(may)g(occur)i(in)e(one)h(single)386 4096 y(perturbation)j(of)h Fv(\030)5 b Fx(.)486 4213 y(The)38 b(follo)n(wing)e(ar)n(gument)i(is)f (complicated)g(by)h(a)h(dif)n(\002culty)e(in)g(case)i(\(ii\).)70 b(If)386 4329 y Fv(\013)q Fw(\()p Fv(Q)p Fw(\))33 b Fx(accumulates)g (on)g Fv(\015)1345 4344 y Fo(v)1419 4329 y Fx(and)h(the)f(holonomy)f (of)h Fv(\015)2357 4344 y Fo(v)2431 4329 y Fx(is)g(repulsi)n(v)o(e)f (on)h(the)g(side)386 4445 y(where)27 b(points)f(of)h Fv(\015)32 b Fx(are)c(pushed)e(to)h(by)f(the)h(dif)n(feomorphism)e Fv(G)i Fx(appearing)f(in)h(the)386 4561 y(proof)i(of)g(Lemma)f(6.3,)i (then)e(it)h(is)f(impossible)f(to)i(say)g(something)e(about)h(the)h(ne) n(w)386 4677 y Fv(!)t Fx(-limit)d(set)h(of)h(lea)n(v)o(es)g(in)f Fv(\013)q Fw(\()p Fv(Q)p Fw(\))h Fx(which)f(accumulated)h(on)f Fv(\015)2553 4692 y Fo(v)2622 4677 y Fx(unless)g Fv(G)h Fx(is)f(chosen)386 4794 y(carefully:)51 b(It)35 b(is)f(possible)g(that) g(lea)n(v)o(es)h(which)f(accumulated)h(on)f Fv(\015)2845 4809 y Fo(v)2921 4794 y Fx(accumulate)386 4910 y(on)c Fv(\015)567 4925 y Fo(v)603 4906 y Fi(0)660 4910 y Fx(when)g(the)g (characteristic)g(foliation)f(is)h(modi\002ed)g(near)g Fv(\015)2721 4925 y Fo(v)2762 4910 y Fx(.)47 b(Ho)n(we)n(v)o(er)29 b(it)g(is)386 5026 y(possible)i(that)h Fv(\015)978 5041 y Fo(v)1014 5022 y Fi(0)1073 5026 y Fx(is)g(also)f(changed)i(when)f Fv(\030)37 b Fx(is)31 b(replaced)i(by)f Fv(\030)2705 4990 y Fn(0)2728 5026 y Fx(.)53 b(Therefore)33 b(one)386 5142 y(has)25 b(to)f(treat)h(all)g Fv(v)31 b Fu(2)d Fv(V)46 b Fx(such)25 b(that)f Fv(\015)1681 5157 y Fo(v)1747 5142 y Fx(belongs)g(to)g(\(i\),\(ii\))h(simultaneously)-6 b(.)486 5259 y(F)o(or)35 b(non-empty)f(open)h(interv)n(als)g Fv(\034)1773 5274 y Fn(\000)1879 5259 y Fu(\032)48 b Fw([)p Fu(\000)p Fw(1)p Fv(;)17 b Fw(0\))35 b Fx(and)h Fv(\034)2545 5274 y Fs(+)2652 5259 y Fu(\032)47 b Fw(\(0)p Fv(;)17 b Fw(1])35 b Fx(we)h(write)391 5375 y Fw(^)-54 b Fv(\034)428 5390 y Fn(\006)487 5375 y Fw(\()p Fv(y)t Fw(\))27 b(:=)h Fu(f)p Fv(y)t Fu(g)21 b(\002)h Fw([)p Fu(\000)p Fw(1)p Fv(;)17 b Fw(1])22 b Fu(\002)p 1440 5320 102 4 v 23 w Fv(\034)1482 5390 y Fn(\006)1566 5375 y Fx(for)j Fv(y)31 b Fu(2)d Fv(\015)5 b Fx(.)31 b(W)-8 b(e)25 b(will)f(\002x)h Fv(\034)2499 5390 y Fn(\006)2584 5375 y Fx(in)f(the)h(follo)n(wing.)486 5491 y(W)-8 b(e)31 b(require)g(that)f Fv(\034)1182 5506 y Fs(+)1272 5491 y Fx(is)h(chosen)f(such)h(that)f(the)h Fv(!)t Fx(-limit)e(of)h(a)i (leaf)f(intersecting)391 5607 y Fw(^)-54 b Fv(\034)428 5622 y Fs(+)487 5607 y Fw(\()p Fv(y)t Fw(\))24 b Fx(is)h(ne)n(v)o(er)f (a)h(hyperbolic)e(singularity)h(for)h(all)f Fv(y)31 b Fu(2)d Fv(X)8 b Fx(.)31 b(Because)p Black Black eop end %%Page: 59 59 TeXDict begin 59 58 bop Black 828 244 a Fq(RIGIDITY)23 b(VERSUS)g(FLEXIBILITY)e(OF)j(TIGHT)g(CONFOLIA)-8 b(TIONS)364 b(59)p Black Black 602 443 a Fu(\017)p Black 41 w Fx(there)25 b(are)h(only)e(\002nitely)g(man)o(y)g(hyperbolic)f(singularities)g(on)i Fv(F)14 b Fx(,)p Black 602 560 a Fu(\017)p Black 41 w Fv(\013)q Fw(\()p Fv(Q)p Fw(\))29 b Fx(intersects)f(e)n(v)o(ery)g (interv)n(al)g(transv)o(erse)g(to)h Fv(\015)2509 575 y Fo(v)2578 560 y Fx(in)g(an)g(open)f(set)h(\(note)693 676 y(that)18 b(there)h(are)h(singular)e(foliations)f(on)i(surf)o(aces) g(with)f(dense)h(quasi-minimal)693 792 y(sets;)38 b(in)33 b(particular)h(stable)g(lea)n(v)o(es)f(of)i(hyperbolic)d(singularities) g(in)i(such)693 908 y(quasi-minimal)23 b(sets)h(may)g(be)h(dense)g(in)f (the)h(surf)o(ace\))h(and)p Black 602 1025 a Fu(\017)p Black 41 w Fv(\013)q Fw(\()p Fv(@)5 b(Q)p Fw(\))26 b Fx(is)f(disjoint)e(from)i(those)g Fv(\015)1913 1040 y Fo(v)1953 1025 y Fv(;)17 b(v)32 b Fu(2)d Fv(V)47 b Fx(which)24 b(intersect)h Fv(\015)31 b Fx(e)n(v)o(en)24 b(if)h Fv(\015)3334 1040 y Fo(v)693 1141 y Fx(is)32 b(quasi-minimal)f(\(this)h(is)g(true)h (because)g(e)n(v)o(ery)f(point)g(of)h Fv(\013)q Fw(\()p Fv(Q)p Fw(\))f Fx(is)h(con-)693 1257 y(nected)g(to)f Fv(H)8 b Fw(\()p Fv(\030)d Fw(\))31 b Fx(by)i(a)g(Le)o(gendrian)f(curv) o(e)g(while)g Fv(\015)38 b Fx(is)32 b(part)g(of)h(the)g(fully)693 1373 y(foliated)24 b(set\))386 1655 y(this)31 b(condition)h(can)g(be)h (satis\002ed.)54 b(Ne)o(xt)31 b(we)i(impose)f(additional)f (restrictions)g(on)386 1772 y Fv(\034)428 1787 y Fn(\000)487 1772 y Fx(:)486 1888 y(W)-8 b(e)21 b(choose)g Fv(\034)977 1903 y Fn(\000)1058 1888 y Fx(such)f(that)h(no)g(point)f(in)26 b Fw(^)-54 b Fv(\034)1920 1903 y Fs(+)1979 1888 y Fw(\()p Fv(x)p Fw(\))22 b Fx(is)e(connected)i(to)j Fw(^)-54 b Fv(\034)2785 1903 y Fn(\000)2845 1888 y Fw(\()p Fv(y)t Fw(\))20 b Fx(for)h Fv(x;)c(y)31 b Fu(2)386 2004 y Fv(X)f Fx(by)21 b(a)h(leaf)g(of)g Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))21 b Fx(which)h(is)f(disjoint)f(from)h Fu(f)p Fw(\()p Fv(y)t(;)c Fw(0\))p Fu(g)11 b(\002)g Fw([sup\()p Fv(\034)2745 2019 y Fn(\000)2804 2004 y Fw(\))p Fv(;)17 b Fw(sup)q(\()p Fv(\034)3113 2019 y Fs(+)3172 2004 y Fw(\)])p Fx(.)30 b(In)386 2120 y(other)25 b(w)o(ords,)g(we)g(require)g (that)g(lea)n(v)o(es)g(of)g Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))24 b Fx(which)h(come)g(from)30 b Fw(^)-54 b Fv(\034)2907 2135 y Fs(+)2966 2120 y Fw(\()p Fv(x)p Fw(\))26 b Fx(do)e(not)386 2237 y(intersect)k Fw(^)-54 b Fv(\034)789 2252 y Fn(\000)848 2237 y Fw(\()p Fv(y)t Fw(\))23 b Fx(when)g(the)o(y)f(meet)h(the)g (piece)h(of)f Fu(f)p Fw(\()p Fv(y)t(;)17 b Fu(\000)p Fw(1\))p Fu(g)f(\002)g Fw([)p Fu(\000)p Fw(1)p Fv(;)h Fw(1])28 b Fu(\032)g Fw(\()p Fv(U)f Fu(\\)16 b Fv(F)e Fw(\))386 2353 y Fx(which)38 b(lies)h(between)f(the)h(lo)n(wer)f (endpoint)g(of)44 b Fw(^)-54 b Fv(\034)2192 2368 y Fn(\000)2251 2353 y Fw(\()p Fv(y)t Fw(\))38 b Fx(and)h(the)f(upper)h(endpoint)386 2469 y(of)j Fw(^)-54 b Fv(\034)548 2484 y Fs(+)607 2469 y Fw(\()p Fv(y)t Fw(\))36 b Fx(for)i(the)f(\002rst)g(time.)66 b(In)37 b(order)g(to)g(satisfy)f(this)g(condition)g(it)g(might)g(be)386 2585 y(necessary)25 b(to)f(shorten)h Fv(\034)1261 2600 y Fs(+)1320 2585 y Fx(.)486 2702 y(There)g(is)g(a)g(choice)h(for)f Fv(\034)1373 2717 y Fs(+)1433 2702 y Fv(;)17 b(\034)1519 2717 y Fn(\000)1603 2702 y Fx(which)25 b(satis\002es)g(these)g (requirements)f(for)i Fv(x;)17 b(y)31 b Fu(2)386 2818 y Fv(X)g Fx(whene)n(v)o(er)23 b(the)h(limit)e(set)h Fv(\015)1448 2833 y Fo(v)1513 2818 y Fx(which)g(corresponds)g(to)g Fv(y)k Fx(is)c(not)g(the)h Fv(!)t Fx(-limit)d(set)j(of)386 2934 y(lea)n(v)o(es)g(intersecting)29 b Fw(^)-54 b Fv(\034)1188 2949 y Fs(+)1247 2934 y Fw(\()p Fv(x)p Fw(\))p Fx(.)486 3050 y(If)32 b Fv(y)k Fx(is)c(contained)g(in)f(a)i(closed)f(leaf)h(of)f Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))p Fx(,)34 b(then)d(one)i(can)f (also)g(satisfy)g(the)386 3166 y(requirement)27 b(for)h Fv(x;)17 b(y)36 b Fu(2)d Fv(X)j Fx(pro)o(vided)26 b(that)h Fv(\034)2037 3181 y Fs(+)2124 3166 y Fx(is)g(so)g(short)g(that)g(the)h (translates)f(of)391 3283 y Fw(^)-54 b Fv(\034)428 3298 y Fs(+)487 3283 y Fw(\()p Fv(x)p Fw(\))32 b Fx(along)f(lea)n(v)o(es)g (of)h Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))30 b Fx(do)i(not)f(co)o(v)o (er)g(the)g(se)o(gment)k Fw(^)-54 b Fv(\034)2624 3298 y Fn(\000)2683 3283 y Fw(\()p Fv(y)t Fw(\))p Fx(\).)50 b(W)-8 b(e)32 b(shorten)386 3399 y Fv(\034)428 3414 y Fs(+)519 3399 y Fx(whene)n(v)o(er)e(this)g(is)h(necessary)-6 b(.)50 b(Finally)-6 b(,)32 b(when)f Fv(y)j Fx(is)d(part)g(of)h(a)f (quasi-minimal)386 3515 y(set)c(and)g(the)h(lea)n(v)o(es)f(of)g Fv(F)14 b Fw(\()p Fv(\030)5 b Fw(\))26 b Fx(which)h(intersect)32 b Fw(^)-54 b Fv(\034)2133 3530 y Fs(+)2193 3515 y Fw(\()p Fv(x)p Fw(\))28 b Fx(accumulate)f(on)g(this)f(quasi-)386 3631 y(minimal)e(set)i(the)g(abo)o(v)o(e)f(requirement)g(can)i(be)f (satis\002ed)g(by)f(shortening)g Fv(\034)3049 3646 y Fn(\006)3135 3631 y Fx(again.)386 3748 y(No)n(w)j(one)g(can)g (construct)g Fv(\034)1380 3763 y Fn(\000)1468 3748 y Fx(in)g(a)h(\002nite)f(number)g(of)g(steps)g(and)g(shortening)f Fv(\034)3215 3763 y Fn(\006)3303 3748 y Fx(at)386 3864 y(each)e(step.)486 3980 y(Let)37 b Fv(t)691 3995 y Fn(\000)803 3980 y Fu(2)52 b Fv(\034)963 3995 y Fn(\000)1023 3980 y Fx(.)70 b(W)-8 b(e)38 b(\002x)h(the)e(dif)n(feomorphism)f Fv(g)55 b Fw(:)e([)p Fu(\000)p Fw(1)p Fv(;)17 b Fw(1])52 b Fu(\000)-17 b(!)52 b Fw([)p Fu(\000)p Fw(1)p Fv(;)17 b Fw(1])38 b Fx(in)386 4096 y(the)30 b(proof)f(of)h(Lemma)f(6.3)h(such) f(that)g Fv(g)34 b Fx(maps)29 b(the)g(entire)h(interv)n(al)f Fw(\()p Fv(t)2910 4111 y Fn(\000)2969 4096 y Fv(;)17 b Fw(sup)q(\()p Fv(\034)3240 4111 y Fs(+)3299 4096 y Fw(\)\))386 4213 y Fx(into)33 b Fv(\034)617 4228 y Fs(+)710 4213 y Fx(and)h(the)f(support)g(of)h Fv(g)j Fx(is)c(contained)g(in)h Fw(\(inf)7 b(\()p Fv(\034)2446 4228 y Fn(\000)2505 4213 y Fw(\))p Fv(;)17 b Fw(sup\()p Fv(\034)2813 4228 y Fs(+)2873 4213 y Fw(\)\))p Fx(.)57 b(The)34 b(role)386 4329 y(of)41 b(the)g(parameters)g Fv(\020)8 b(;)17 b(\020)1297 4293 y Fn(0)1360 4329 y Fx(from)41 b(the)g(proof)g(of)g(Lemma)g(6.3)f(is)h (no)n(w)f(played)h(by)386 4445 y Fw(sup)q(\()p Fv(\034)613 4460 y Fs(+)672 4445 y Fw(\))p Fv(;)17 b Fw(inf)7 b(\()p Fv(\034)952 4460 y Fn(\000)1011 4445 y Fw(\))p Fx(.)486 4561 y(If)33 b Fv(\030)k Fx(is)32 b(modi\002ed)g(by)h(the)f(procedure)h (described)g(in)f(the)h(proof)f(of)h(Lemma)f(6.3)386 4677 y(using)c(the)i(dif)n(feomorphism)c Fv(g)33 b Fx(chosen)c(abo)o(v) o(e,)h(then)f(one)g(obtains)g(a)g(confoliation)386 4794 y Fv(\030)434 4758 y Fn(0)478 4794 y Fx(such)21 b(that)f(all)h(lea)n(v) o(es)g(of)g Fv(F)14 b Fw(\()p Fv(\030)1507 4758 y Fn(0)1529 4794 y Fw(\))21 b Fx(starting)f(at)h(the)g(elliptic)f(singularity)g(in) g(the)h(center)386 4910 y(of)29 b(the)g(original)f(o)o(v)o(ertwisted)g (whose)g Fv(!)t Fx(-limit)f(set)i(w)o(as)h Fv(\015)2453 4925 y Fo(v)2522 4910 y Fx(such)f(that)g Fv(\015)2964 4925 y Fo(v)3030 4910 y Fu(\\)d Fv(\015)40 b Fu(6)p Fw(=)c Fu(;)386 5026 y Fx(ne)n(v)o(er)24 b(meet)h(a)g(hyperbolic)e (singularity)g(of)i Fv(F)14 b Fw(\()p Fv(\030)2088 4990 y Fn(0)2111 5026 y Fw(\))p Fx(.)486 5142 y(Since)26 b(all)f(elliptic)g (singularities)f(on)h(the)h(boundary)f(of)h(the)f(basin)h(of)f(the)h (elliptic)386 5259 y(singularity)g(in)i Fv(\013)q Fw(\()p Fv(Q)p Fw(\))g Fx(are)g(automatically)f(ne)o(gati)n(v)o(e)e(and)j(all)g (hyperbolic)f(singular)n(-)386 5375 y(ities)g(on)i(the)f(boundary)f(of) i(the)f(basin)g(where)h(already)f(present)h(in)e Fv(\013)q Fw(\()p Fv(@)5 b(Q)p Fw(\))30 b Fx(there)e(is)386 5491 y(an)j(o)o(v)o(ertwisted)e(star)i Fw(\()p Fv(Q)1294 5455 y Fn(0)1318 5491 y Fv(;)17 b(V)1440 5455 y Fn(0)1463 5491 y Fv(;)g(\013)1570 5455 y Fn(0)1593 5491 y Fw(\))31 b Fx(and)g Fv(V)1916 5455 y Fn(0)1970 5491 y Fx(can)h(be)f(vie)n(wed)f (as)h(a)h(subset)e(of)h Fv(V)53 b Fx(by)386 5607 y(construction.)29 b(Moreo)o(v)o(er)l(,)24 b Fu(jE)9 b Fw(\()p Fv(\030)1546 5571 y Fn(0)1568 5607 y Fw(\))p Fu(j)27 b Fv(<)h Fu(jE)9 b Fw(\()p Fv(\030)c Fw(\))p Fu(j)p Fx(.)1265 b Fl(\003)p Black Black eop end %%Page: 60 60 TeXDict begin 60 59 bop Black 386 244 a Fq(60)1256 b(T)-6 b(.)19 b(V)m(OGEL)p Black 486 443 a Fx(No)n(w)32 b(we)i(can)g (\002nally)f(sho)n(w)g(that)g(there)h(are)g(no)f(o)o(v)o(ertwisted)f (stars)h(when)g Fv(\030)38 b Fx(is)386 560 y(symplectically)23 b(\002llable.)p Black 386 756 a FD(Theor)n(em)28 b(6.9.)p Black 41 w Ft(Let)f Fw(\()p Fv(M)5 b(;)17 b(\030)5 b Fw(\))26 b Ft(be)g(a)g Fv(C)1709 720 y Fo(k)1751 756 y Ft(-confoliation,)f Fv(k)33 b Fu(\025)e Fw(2)p Ft(,)26 b(whic)o(h)g(is)f(symplecti-)386 872 y(cally)j(\002llable)o(.)40 b(Then)29 b(no)g(oriented)e(embedded)i(surface)f(contains)f(an)h(o)o (vertwisted)386 988 y(star)-11 b(.)p Black 386 1185 a(Pr)l(oof)o(.)p Black 39 w Fx(Let)25 b Fw(\()p Fv(X)r(;)17 b(!)t Fw(\))24 b Fx(be)h(a)h(symplectic)d(\002lling)i(of)g Fv(\030)5 b Fx(.)30 b(Assume)24 b(that)h Fv(F)38 b Fx(is)25 b(an)g(embed-)386 1301 y(ded)h(surf)o(ace)h(containing)e(an)h(o)o(v)o(ertwisted)e(star)i Fw(\()p Fv(Q;)17 b(V)5 b(;)17 b(\013)q Fw(\))p Fx(.)35 b(It)26 b(is)f(suf)n(\002cient)h(to)g(treat)386 1417 y(only)g(the)h(case)g(of)g(closed)f(surf)o(aces)h(when)g(the)g (elliptic)e(singularity)g(in)i(the)f(interior)386 1534 y(of)f Fv(\013)q Fw(\()p Fv(Q)p Fw(\))g Fx(is)f(positi)n(v)o(e.)486 1650 y(In)f(the)g(\002rst)g(part)g(of)g(the)g(proof)g(we)h(sho)n(w)e (ho)n(w)g(to)h(reduce)h(the)f(number)f(of)i(virtual)386 1766 y(v)o(ertices.)k(Because)21 b(o)o(v)o(ertwisted)c(stars)i(are)h (not)f(required)g(to)g(be)h(injecti)n(v)o(e)e(as)h(Le)o(gen-)386 1882 y(drian)27 b(polygons,)e(we)j(sho)n(w)d(in)i(a)g(second)g(step)f (ho)n(w)g(to)h(obtain)f(an)h(embedded)f(disc)386 1998 y Fv(D)36 b Fx(such)d(that)g Fv(@)5 b(D)37 b Fx(is)c(Le)o(gendrian)g (and)g Fv(T)14 b(D)s Fu(j)2022 2013 y Fo(@)t(D)2160 1998 y Fx(is)33 b(transv)o(erse)g(to)g Fv(\030)5 b Fu(j)2883 2013 y Fo(@)t(D)3020 1998 y Fx(violating)386 2115 y(De\002nition)26 b(1.3)h(starting)f(from)g(an)h(o)o(v)o(ertwisted)e(star)i Fw(\()p Fv(Q;)17 b Fu(;)p Fv(;)g(\013)q Fw(\))p Fx(.)36 b(The)27 b(confoliation)386 2231 y(is)22 b(modi\002ed)g(se)n(v)o(eral)g (times)f(b)n(ut)h(all)h(confoliations)d(appearing)j(in)f(the)h(proof)f (will)g(be)386 2347 y Fv(C)463 2311 y Fs(0)502 2347 y Fx(-close)30 b(to)g Fv(\030)5 b Fx(.)45 b(In)30 b(particular)f(the)o(y) g(are)i(symplectically)d(\002llable.)45 b(Therefore)31 b(the)386 2463 y(assumption)21 b(that)h Fw(\()p Fv(M)5 b(;)17 b(\030)5 b Fw(\))23 b Fx(admits)e(an)j(o)o(v)o(ertwisted)c(star) j(contradicts)g(Theorem)f(1.4.)486 2580 y(Notice)k(that)h(in)g(the)g (presence)h(of)f(an)g(o)o(v)o(ertwisted)e(star)j Fv(\030)j Fx(cannot)c(be)h(a)f(foliation)386 2696 y(e)n(v)o(erywhere.)j (Therefore)25 b Fv(M)35 b Fx(is)23 b(not)g(a)h(minimal)f(set)g(of)h (the)g(fully)f(foliated)g(part)h(of)g Fv(\030)386 2812 y Fx(and)h Fv(\030)k Fx(is)24 b(not)h(a)g(foliation)e(without)h (holonomy)-6 b(.)486 2928 y Ft(Step)31 b(1:)45 b(If)31 b Fv(V)62 b Fu(6)p Fw(=)40 b Fu(;)p Ft(,)34 b(then)d Fv(\030)36 b Ft(can)c(be)g(appr)l(oximated)d(by)j(a)g(confoliation)d (whic)o(h)386 3045 y(admits)24 b(an)g(o)o(vertwisted)g(star)g(with)h (less)f(virtual)g(vertices)h(than)f Fw(\()p Fv(Q;)17 b(V)5 b(;)17 b(\013)q Fw(\))p Ft(.)486 3161 y Fx(W)-8 b(e)37 b(\002x)h Fv(v)843 3176 y Fs(0)933 3161 y Fu(2)51 b Fv(V)22 b Fx(.)68 b(If)37 b Fv(\015)1376 3176 y Fs(0)1466 3161 y Fw(:=)51 b Fv(\015)1671 3176 y Fo(v)1705 3185 y Fk(0)1781 3161 y Fx(intersects)36 b Fv(H)8 b Fw(\()p Fv(\030)d Fw(\))p Fx(,)39 b(then)e(an)h(application)e(of)386 3277 y(Lemma)d(3.6)h(yields)e(a)j(surf)o(ace)f(carrying)g(an)g(o)o(v)o (ertwisted)e(star)h(with)g(less)h(virtual)386 3393 y(v)o(ertices.)c(No) n(w)24 b(assume)g Fv(\015)1335 3408 y Fs(0)1397 3393 y Fu(\\)e Fv(H)8 b Fw(\()p Fv(\030)d Fw(\))27 b(=)g Fu(;)p Fx(.)486 3509 y(Let)43 b Fv(L)h Fx(be)f(the)g(maximal)f(connected)i (open)f(immersed)f(hypersurf)o(ace)i(of)f Fv(M)386 3626 y Fx(which)35 b(is)g(tangent)g(to)g Fv(\030)40 b Fx(and)c(contains)f Fv(\015)1891 3641 y Fs(0)1930 3626 y Fx(.)63 b(If)36 b Fv(L)48 b Fw(=)f Fu(;)p Fx(,)38 b(then)d(there)h(is)f(a)h(Le)o(gen-) 386 3742 y(drian)e(se)o(gment)e Fv(\033)38 b Fx(satisfying)33 b(the)g(hypothesis)f(of)i(Lemma)f(6.4.)58 b(After)34 b(applying)386 3858 y(this)i(lemma,)k Fv(\015)955 3873 y Fo(v)1033 3858 y Fx(intersects)d(the)g(contact)g(re)o(gion)g(of)g (the)g(modi\002ed)g(confoliation)386 3974 y(and)25 b(we)g(are)g(done.) 486 4091 y(No)n(w)38 b(assume)g Fv(L)54 b Fu(6)p Fw(=)g Fu(;)39 b Fx(and)g(let)f Fv(L)1774 4054 y Fn(1)1888 4091 y Fx(be)h(the)g(space)g(of)g(ends)g(of)g Fv(L)p Fx(.)74 b(W)-8 b(e)39 b(say)386 4207 y(that)c(an)g(end)g Fv(e)47 b Fu(2)g Fv(L)1150 4171 y Fn(1)1261 4207 y Fx(lies)34 b(in)h Fv(H)8 b Fw(\()p Fv(\030)d Fw(\))34 b Fx(if)h(for)g(e)n(v)o(ery) g(compact)g(set)g Fv(K)54 b Fu(\032)47 b Fv(L)36 b Fx(there)386 4323 y(is)g(a)h(Le)o(gendrian)f(curv)o(e)g(from)h Fv(H)8 b Fw(\()p Fv(\030)d Fw(\))35 b Fx(to)h(the)h(connected)g(component)e (of)i Fv(L)31 b Fu(n)g Fv(K)386 4439 y Fx(corresponding)24 b(to)g Fv(e)h Fx(and)g(the)g(curv)o(e)f(a)n(v)n(oids)g Fv(K)7 b Fx(.)486 4556 y Ft(Step)23 b(1a:)30 b(If)24 b Fv(L)995 4519 y Fn(1)1098 4556 y Fu(6)p Fw(=)j Fu(;)p Ft(,)d(then)f(we)i(appr)l(oximate)d Fv(\030)28 b Ft(suc)o(h)23 b(that)g(all)g(ends)g(of)h Fv(L)g Ft(lies)f(in)386 4672 y(the)i(contact)f(r)l(e)l(gion)g(of)h(the)f(modi\002ed)g(confoliation.) 486 4788 y Fx(The)j(set)g(of)g(ends)g(in)g Fv(H)8 b Fw(\()p Fv(\030)d Fw(\))27 b Fx(is)g(open)g(in)g Fv(L)1957 4752 y Fn(1)2032 4788 y Fx(,)h(therefore)g(its)e(complement)g Fv(L)3179 4752 y Fn(1)3179 4814 y Fo(f)7 b(ol)3308 4788 y Fx(is)386 4910 y(compact.)42 b(T)-8 b(o)29 b(each)g Fv(e)35 b Fu(2)h Fv(L)1382 4874 y Fn(1)1382 4936 y Fo(f)7 b(ol)1512 4910 y Fx(we)29 b(associate)g(a)g(minimal)e(set)h Fu(M)p Fw(\()p Fv(e)p Fw(\))35 b Fu(\032)h Fw(lim)3143 4925 y Fo(e)3196 4910 y Fv(L)30 b Fx(of)386 5026 y(the)e(fully)f (foliated)h(part)g(of)g Fv(\030)33 b Fx(\(this)28 b(is)f(e)o(xplained)g (in)h([4],)h(p.)41 b(115\).)f(Recall)29 b(that)f Fv(M)386 5142 y Fx(cannot)i(be)h(a)g(minimal)d(set)j(of)f(the)h(fully)e (foliated)h(part)h(of)f Fv(\030)5 b Fx(.)48 b(According)30 b(to)g([18],)386 5259 y(p.19,)e(all)g(minimal)f(sets)h(are)h(either)f (closed)g(lea)n(v)o(es)f(or)i(e)o(xceptional)e(minimal)f(sets.)386 5375 y(Note)e(that)h Fv(L)g Fx(may)g(be)g(contained)f(in)g Fu(M)p Fw(\()p Fv(e)p Fw(\))p Fx(.)486 5491 y(If)36 b Fu(M)p Fw(\()p Fv(e)p Fw(\))h Fx(is)e(a)i(closed)f(leaf)h(of)f Fv(\030)41 b Fx(whose)36 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b(iterate)g(the)g(procedure)h(from)f(the)g(v)o(ery)f (be)o(ginning)g(with)g Fv(v)2733 2318 y Fs(0)2803 2303 y Fu(2)30 b Fv(V)2978 2267 y Fn(0)3027 2303 y Fx(and)d(with)386 2419 y(an)33 b(inte)o(gral)e(surf)o(ace)i(of)g Fv(\030)1331 2383 y Fn(0)1386 2419 y Fx(containing)f Fv(\015)1896 2383 y Fn(0)1891 2444 y Fs(0)1930 2419 y Fx(.)54 b(Since)33 b Fu(E)9 b Fw(\()p Fv(\030)c Fw(\))31 b Fx(is)h(\002nite)h(and)f Fu(jE)9 b Fw(\()p Fv(\030)3169 2383 y Fn(0)3191 2419 y Fw(\))p Fu(j)42 b Fv(<)386 2536 y Fu(jE)9 b Fw(\()p Fv(\030)c Fw(\))p Fu(j)23 b Fx(this)h(phenomenon)f(can)j(occur)f(only)f (\002nitely)g(man)o(y)g(times.)486 2652 y(In)j(later)h(applications)f (of)h(the)f(abo)o(v)o(e)g(construction)f Fv(\015)2410 2616 y Fn(0)2405 2676 y Fs(0)2478 2652 y Fw(=)33 b Fv(\015)2638 2667 y Fs(0)2705 2652 y Fx(and)27 b(the)h(maximal)386 2768 y(inte)o(gral)38 b(surf)o(ace)i(of)f Fv(\030)1224 2732 y Fn(0)1286 2768 y Fx(containing)e Fv(\015)1801 2732 y Fn(0)1796 2793 y Fs(0)1875 2768 y 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