Verfügbarkeit: Fine structures of hyperbolic diffeomorphisms

Fine structures of hyperbolic diffeomorphisms:

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Bibliographische Detailangaben
Beteiligte Personen:	Pinto, Alberto Adrego 1964- (VerfasserIn), Rand, David A. (VerfasserIn), Ferreira, Flávio P. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin ; Heidelberg Springer-Verlag 2009
Schriftenreihe:	Springer monographs in mathematics
Schlagwörter:	Hyperbolizität Dynamisches System Diffeomorphismus
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017117514&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XVI, 353 Seiten Diagramme
ISBN:	9783540875246

Internformat

MARC


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Datensatz im Suchindex

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adam_text	Contents Introduction ............................................... 1 1.1 Stable and unstable leaves ................................ 1 1.2 Marking ................................................ 3 1.3 Metric ................................................. 4 1.4 Interval notation ........................................ 5 1.5 Basic holonomies ........................................ 6 1.6 Foliated atlas ........................................... 6 1.7 Foliated atlas Al(g, p) .................................... 8 1.8 Straightened graph-like charts ............................. 10 1.9 Orthogonal atlas ........................................ 17 1.10 Further literature ........................................ 19 HR structures ............................................. 21 2.1 Conjugacies ............................................. 21 2.2 HR - Holder ratios ....................................... 22 2.3 Foliated atlas A(r) ...................................... 23 2.4 Invariants .............................................. 25 2.5 HR Orthogonal atlas ..................................... 27 2.6 Complete invariant ...................................... 28 2.7 Moduli space ........................................... 33 2.8 Further literature ........................................ 36 Solenoid functions ......................................... 37 3.1 Realized solenoid functions ............................... 37 3.2 Holder continuity ........................................ 38 3.3 Matching condition ...................................... 38 3.4 Boundary condition ...................................... 39 3.5 Scaling function ......................................... 40 3.6 Cylinder-gap condition ................................... 41 3.7 Solenoid functions ....................................... 41 3.8 Further literature ........................................ 43 XII Contents 4 Self-renormałłzable structures ............................. 45 4.1 Train-tracks ............................................ 45 4.2 Charts ................................................. 47 4.3 Markov maps ........................................... 47 4.4 Exchange pseudo-groups ................................. 48 4.5 Markings ............................................... 49 4.6 Self-renormalizable structures ............................. 51 4.7 Hyperbolic diffeomorphisms ............................... 52 4.8 Explosion of smoothness .................................. 52 4.9 Further literature ........................................ 53 5 Rigidity ................................................... 55 5.1 Complete sets of holonomies .............................. 55 5.2 C1 1 diffeomorphisms .................................... 58 5.3 C1 11^ and cross-ratio distortions for ratio functions ......... 59 5.4 Fundamental Rigidity Lemma ............................. 62 5.5 Existence of affine models ................................ 65 5.6 Proof of the hyperbolic and Anosov rigidity ................. 67 5.7 Twin leaves for codimension 1 attractors ................... 68 5.8 Non-existence of affine models ............................. 70 5.9 Non-existence of uniformly C1 1101 complete sets of holonomies for codimension 1 attractors .................... 71 5.10 Further literature ........................................ 72 6 Gibbs measures ............................................ 73 6.1 Dual symbolic sets ....................................... 73 6.2 Weighted scaling function and Jacobian .................... 74 6.3 Weighted ratio structure ................................. 75 6.4 Gibbs measure and its dual ............................... 76 6.5 Further literature ........................................ 84 7 Measure scaling functions .................................. 85 7.1 Gibbs measures ......................................... 85 7.2 Extended measure scaling function ........................ 86 7.3 Further literature ........................................ 92 8 Measure solenoid functions ................................ 93 8.1 Measure solenoid functions ............................... 93 8.1.1 Cylinder-cylinder condition ......................... 94 8.2 Measure ratio functions .................................. 95 8.3 Natural geometric measures ............................... 96 8.4 Measure ratio functions and self-renormalizable structures .... 99 8.5 Dual measure ratio function ..............................104 8.6 Further literature ........................................106 Contents XIII 9 Cocycle-gap pairs ..........................................107 9.1 Measure-length ratio cocycle ..............................107 9.2 Gap ratio function .......................................109 9.3 Ratio functions ..........................................109 9.4 Cocycle-gap pairs ........................................ Ill 9.5 Further literature ........................................117 10 Hausdorff realizations ......................................119 10.1 One-dimensional realizations of Gibbs measures .............119 10.2 Two-dimensional realizations of Gibbs measures .............122 10.3 Invariant Hausdorff measures .............................127 10.3.1 Moduli space SOL1 ................................131 10.3.2 Moduli space of cocycle-gap pairs ...................132 10.3.3 ¿¿.-bounded solenoid equivalence class of Gibbs measures 132 10.4 Further literature ........................................134 11 Extended Livsic-Sinai eigenvalue formula ..................135 11.1 Extending the eigenvalues s result of De la Llave, Marco and Moriyon ................................................135 11.2 Extending the eigenvalue formula of A. N. Livšic and Ja. G. Sinai ...................................................140 11.3 Further literature ........................................141 12 Arc exchange systems and renormalization ................143 12.1 Arc exchange systems ....................................143 12.1.1 Induced arc exchange systems .......................145 12.2 Renormalization of arc exchange systems ...................148 12.2.1 Renormalization of induced arc exchange systems .....150 12.3 Markov maps versus renormalization .......................152 12.4 C1+H flexibility .........................................155 12.5 Сг но rigidity ..........................................156 12.6 Further literature ........................................159 13 Golden tilings (in collaboration with J.P. Almeida and A. Portela) ................................................161 13.1 Golden difeomorphisms ..................................161 13.1.1 Golden train-track .................................162 13.1.2 Golden arc exchange systems .......................163 13.1.3 Golden renormalization ............................165 13.1.4 Golden Markov maps ..............................167 13.2 Anosov diffeomorphisms ..................................168 13.2.1 Golden diffeomorphisms ............................169 13.2.2 Arc exchange system ...............................170 13.2.3 Markov maps .....................................172 13.2.4 Exchange pseudo-groups ...........................173 XIV Contents 13.2.5 Self-renormalizable structures .......................174 13.3 HR structures ...........................................174 13.4 Fibonacci decomposition .................................175 13.4.1 Matching condition ................................176 13.4.2 Boundary condition ................................176 13.4.3 The exponentially fast Fibonacci repetitive property .. . 177 13.4.4 Golden tilings .....................................177 13.4.5 Golden tilings versus solenoid functions ..............178 13.4.6 Golden tilings versus Anosov diffeomorphisms .........181 13.5 Further literature ........................................182 14 Pseudo- Anosov diffeomorphisms in pseudo-surfaces ........183 14.1 Affine pseudo-Anosov maps ...............................183 14.2 Paper models Ą ........................................184 14.3 Pseudo-linear algebra ....................................186 14.4 Pseudo-differentiable maps ...............................191 14.4.1 Cr pseudo-manifolds ...............................194 14.4.2 Pseudo-tangent spaces .............................195 14.4.3 Pseudo-inner product onĄ ........................195 14.5 Cr foliations ............................................198 14.6 Further literature ........................................199 A Appendix A: Classifying C1+ structures on the real line ... 201 A.I The grid ...............................................201 A. 2 Cross-ratio distortion of grids .............................202 A.3 Quasisymmetric homeomorphisms .........................204 A.4 Horizontal and vertical translations of ratio distortions .......207 A. 5 Uniformly asymptotically affine (uaa) homeomorphisms ......214 A.6 C1+r diffeomorphisms ....................................224 A.7 C2+r diffeomorphisms ....................................228 A. 8 Cross-ratio distortion and smoothness ......................232 A.9 Further literature ........................................233 В Appendix B: Classifying C1+ structures on Cantor sets .... 235 B.I Smooth structures on trees ...............................235 B.I.I Examples ........................................236 B.2 Basic definitions .........................................239 B.3 (1 + a)-contact equivalence ...............................240 B.3.1 (1 + a) scale and contact equivalence ................241 B.3.2 A refinement of the equivalence property .............242 B.3.3 The map Lt ......................................243 B.3.4 The definition of the contact and gap maps ...........246 B.3.5 The map Ln ......................................247 B.3. 6 The sequence of maps Ln converge ..................247 B.3.7 The map !„ .....................................251 Contents XV В. 3.8 Sufficient condition for C1+a~-equivalent .............252 B.3.9 Necessary condition for CXJra -equivalent ............252 B.4 Smooth structures with α -controlled geometry and bounded geometry ...............................................254 B.4.1 Bounded geometry ................................257 B.5 Further literature ........................................259 С Appendix C: Expanding dynamics of the circle ............261 C.I C1+Hblder structures U for the expanding circle map E .......261 C.2 Solenoids (Ě,Š) ..........................................263 C.3 Solenoid functions s:C~^R+ ............................265 C.4 d-Adic tilings and grids ..................................267 C.5 Soienoidal charts for the C1+Hölder expanding circle map E ... 269 С. 6 Smooth properties of soienoidal charts .....................271 C.7 A Teichmüller space .....................................272 C.8 Sullivan s soienoidal surfaces ..............................273 C.9 (Uaa) structures U for the expanding circle map E ..........274 С. 10 Regularities of the soienoidal charts ........................275 C.ll Further literature ........................................277 D Appendix D: Markov maps on train-tracks ................279 D.I Cookie-cutters ..........................................279 D.2 Pronged singularities in pseudo-Anosov maps ...............280 D.3 Train-tracks ............................................281 D.3.1 Train-track obtained by glueing .....................282 D.4 Markov maps ...........................................283 D.5 The scaling function .....................................286 D.5.1 A Holder scaling function without a corresponding smooth Markov map ...............................290 D.6 Smoothness of Markov maps and geometry of the cylinder structures ..............................................291 D.6.1 Solenoid set ......................................291 D.6.2 Pre-solenoid functions ..............................292 D.6.3 The solenoid property of a cylinder structure .........293 D.6.4 The solenoid equivalence between cylinder structures. .. 295 D.7 Solenoid functions .......................................297 D.7.1 Turntable condition ................................298 D.7.2 Matching condition ................................298 D.8 Examples of solenoid functions for Markov maps ............299 D.8.1 The horocycle maps and the diffeomorphisms of the circle .............................................300 D.8.2 Connections of a smooth Markov map ................301 D.9 «-solenoid functions ......................................302 D.10 Canonical set С of charts .................................303 D.ll One-to-one correspondences ...............................305 XVI Contents D. 12 Existence of eigenvalues for (uaa) Markov maps .............307 D.13 Further literature ........................................311 E Appendix E: Explosion of smoothness for Markov families . 313 E.I Markov families on train-tracks ............................313 E.I.I Train-tracks ......................................313 E.1.2 Markov families ...................................314 E.1.3 (Uaa) Markov families .............................315 E.1.4 Bounded Geometry ................................318 E.2 (Uaa) conjugacies .......................................319 E.3 Canonical charts ........................................324 E.4 Smooth bounds for Cr Markov families .....................325 E.4.1 Arzelà-Ascoli Theorem .............................330 E.5 Smooth conjugacies ......................................331 E.6 Further literature ........................................334 References .....................................................335 Index ..........................................................347
any_adam_object	1
author	Pinto, Alberto Adrego 1964- Rand, David A. Ferreira, Flávio P.
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discipline	Mathematik
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indexdate	2024-12-20T13:28:18Z
institution	BVB
isbn	9783540875246
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-017117514
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owner	DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-83
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physical	XVI, 353 Seiten Diagramme
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publisher	Springer-Verlag
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series2	Springer monographs in mathematics
spellingShingle	Pinto, Alberto Adrego 1964- Rand, David A. Ferreira, Flávio P. Fine structures of hyperbolic diffeomorphisms Hyperbolizität (DE-588)4710615-3 gnd Dynamisches System (DE-588)4013396-5 gnd Diffeomorphismus (DE-588)4149767-3 gnd
subject_GND	(DE-588)4710615-3 (DE-588)4013396-5 (DE-588)4149767-3
title	Fine structures of hyperbolic diffeomorphisms
title_auth	Fine structures of hyperbolic diffeomorphisms
title_exact_search	Fine structures of hyperbolic diffeomorphisms
title_full	Fine structures of hyperbolic diffeomorphisms Alberto A. Pinto ; David A. Rand ; Flávio Ferreira
title_fullStr	Fine structures of hyperbolic diffeomorphisms Alberto A. Pinto ; David A. Rand ; Flávio Ferreira
title_full_unstemmed	Fine structures of hyperbolic diffeomorphisms Alberto A. Pinto ; David A. Rand ; Flávio Ferreira
title_short	Fine structures of hyperbolic diffeomorphisms
title_sort	fine structures of hyperbolic diffeomorphisms
topic	Hyperbolizität (DE-588)4710615-3 gnd Dynamisches System (DE-588)4013396-5 gnd Diffeomorphismus (DE-588)4149767-3 gnd
topic_facet	Hyperbolizität Dynamisches System Diffeomorphismus
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017117514&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT pintoalbertoadrego finestructuresofhyperbolicdiffeomorphisms AT randdavida finestructuresofhyperbolicdiffeomorphisms AT ferreiraflaviop finestructuresofhyperbolicdiffeomorphisms

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