Verfügbarkeit: Hyperbolic flows | Technische Universität München

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Bibliographische Detailangaben
Beteiligte Personen:	Fisher, Todd (VerfasserIn), Hasselblatt, Boris 1961- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin European Mathematical Society [2019]
Schriftenreihe:	Zurich lectures in advanced mathematics
Schlagwörter:	Dynamisches System Hyperbolisches Differentialgleichungssystem Hyperbolisches System Ergodische Kette Anosov flow Axiom A Markov partitions entropy equilibrium states ergodic theory expansiveness geodesic flow hyperbolicity rigidity shadowing specification stable manifold symbolic flows topological dynamics topological pressure
Links:	http://digitale-objekte.hbz-nrw.de/storage2/2020/10/01/file_8/8922272.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032987005&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	xiv, 723 Seiten Illustrationen 24 cm x 17 cm
ISBN:	9783037192009 3037192003

Internformat

MARC


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Datensatz im Suchindex

_version_	1819372040234205184
adam_text	CONTENTS ACKNOWLEDGMENTS .................................................................................................. VII 0 INTRODUCTION ...................................................................................................... 1 0.1 ABOUT THIS BOOK ..................................................................................... 1 0.2 CONTINUOUS AND DISCRETE TIME ................................................................ 3 0.3 HISTORICAL SKETCH .................................................................................. 6 I FLOWS .................................................................................................................. 15 1 TOPOLOGICAL DYNAMICS ..................................................................................... 19 1.1 BASIC PROPERTIES ..................................................................................... 19 1.2 TIME CHANGE, FLOW UNDER A FUNCTION, AND SECTIONS ............................ 34 1.3 CONJUGACY AND ORBIT EQUIVALENCE ......................................................... 39 1.4 ATTRACTORS AND REPELLERS ......................................................................... 48 1.5 RECURRENCE PROPERTIES AND CHAIN DECOMPOSITION ................................ 60 1.6 TRANSITIVITY, MINIMALITY, AND TOPOLOGICAL MIXING ................................ 78 1.7 EXPANSIVE FLOWS ..................................................................................... 88 1.8 WEAKENING EXPANSIVITY* ..................................................................... 94 1.9 SYMBOLIC FLOWS, CODING ......................................................................... 98 2 HYPERBOLIC GEODESIC FLOW* ................................................................................ 113 2.1 ISOMETRIES, GEODESICS, AND HOROCYCLES OF THE HYPERBOLIC PLANE AND DISK 113 2.2 DYNAMICS OF THE NATURAL FLOWS ................................................................ 120 2.3 COMPACT FACTORS ......................................................................................... 129 2.4 THE GEODESIC FLOW ON COMPACT HYPERBOLIC SURFACES ......................... 131 2.5 SYMMETRIC SPACES ...................................................................................... 136 2.6 HAMILTONIAN SYSTEMS ............................................................................ 141 3 ERGODIC THEORY ................................................................................................... 155 3.1 FLOW-INVARIANT MEASURES AND MEASURE-PRESERVING TRANSFORMATIONS . 155 XII CONTENTS 3.2 ERGODIC THEOREMS ....................................................................................... 163 3.3 ERGODICITY ............................................................................................... 171 3.4 MIXING ...................................................................................................... 179 3.5 INVARIANT MEASURES UNDER TIME CHANGE .................................................... 194 3.6 FLOWS UNDER A FUNCTION ............................................................................. 196 3.7 SPECTRAL THEORY* ......................................................................................... 203 4 ENTROPY, PRESSURE, AND EQUILIBRIUM STATES .......................................................... 211 4.1 MEASURE-THEORETIC ENTROPY ....................................................................... 211 4.2 TOPOLOGICAL ENTROPY ................................................................................... 216 4.3 TOPOLOGICAL PRESSURE AND EQUILIBRIUM STATES .......................................... 232 4.4 EQUILIBRIUM STATES FOR TIME-T MAPS* ....................................................... 243 II HYPERBOLIC FLOWS ...............................................................................................247 INTRODUCTION TO PART II ................................................................................................ 249 5 HYPERBOLICITY ...................................................................................................... 251 5.1 HYPERBOLIC SETS AND BASIC PROPERTIES ...................................................... 252 5.2 PHYSICAL FLOWS: GEODESIC FLOWS, MAGNETIC FLOWS, BILLIARDS, GASES, AND LINKAGES ...................................................................................................... 263 5.3 SHADOWING, EXPANSIVITY, CLOSING, SPECIFICATION, AND AXIOM A .... 293 5.4 THE ANOSOV SHADOWING THEOREM, STRUCTURAL AND Q-STABILITY .... 309 5.5 LOCAL LINEARIZATION: THE HARTMAN-GROBMAN THEOREM ....................... 322 5.6 THE MATHER-MOSER METHOD* ...................................................................324 6 INVARIANT FOLIATIONS ............................................................................................. 331 6.1 STABLE AND UNSTABLE FOLIATIONS ...................................................................332 6.2 GLOBAL FOLIATIONS, LOCAL MAXIMALITY, BOWEN BRACKET .............................336 6.3 LIVSHITZ THEORY ......................................................................................... 348 6.4 HOLDER CONTINUITY OF ORBIT EQUIVALENCE ...................................................352 6.5 HORSESHOES AND ATTRACTORS .......................................................................... 355 6.6 MARKOV PARTITIONS ...................................................................................... 363 6.7 FAILURE OF LOCAL MAXIMALITY* ................................................................... 371 6.8 SMOOTH LINEARIZATION AND NORMAL FORMS* ................................................374 6.9 DIFFERENTIABILITY IN THE HARTMAN-GROBMAN THEOREM* .......................... 390 7 ERGODIC THEORY OF HYPERBOLIC SETS .......................................................................399 7.1 THE HOPF ARGUMENT, ABSOLUTE CONTINUITY, MIXING ..................................... 400 CONTENTS XIII 7.2 STABLE ERGODICITY* ...................................................................................... 410 7.3 SPECIFICATION, UNIQUENESS OF EQUILIBRIUM STATES ................................... 420 7.4 SINAI-RUELLE-BOWEN MEASURES ................................................................435 7.5 HAMENSTADT-MARGULIS MEASURE* ............................................................ 446 7.6 ASYMPTOTIC ORBIT GROWTH* ......................................................................453 7.7 RATES OF MIXING* ...................................................................................... 461 8 ANOSOV FLOWS ...................................................................................................... 471 8.1 ANOSOV DIFFEOMORPHISMS, SUSPENSIONS, AND MIXING .............................. 472 8.2 FOULON-HANDEL-THURSTON SURGERY ......................................................... 476 8.3 ANOMALOUS ANOSOV FLOWS ......................................................................... 486 8.4 CODIMENSION- 1 ANOSOV FLOWS ................................................................493 8.5 {^-COVERED ANOSOV 3 -FLOWS ...................................................................... 502 8.6 HOROCYCLE AND UNSTABLE FLOWS* ................................................................509 9 RIGIDITY ............................................................................................................... 531 9.1 MULTIDIMENSIONAL TIME: COMMUTING FLOWS ............................................. 533 9.2 CONJUGACIES ............................................................................................... 543 9.3 ENTROPY AND LYAPUNOV EXPONENTS .............................................................548 9.4 OPTIMAL REGULARITY OF THE INVARIANT SUBBUNDLES ...................................... 553 9.5 LONGITUDINAL REGULARITY ............................................................................562 9.6 SHARPNESS FOR TRANSVERSELY SYMPLECTIC FLOWS, THREADING ....................... 566 9.7 SMOOTH INVARIANT FOLIATIONS ...................................................................... 572 9.8 GODBILLON-VEY INVARIANTS* ...................................................................... 582 APPENDICES A MEASURE-THEORETIC ENTROPY OF MAPS ................................................................... 591 A.L LEBESGUE SPACES ..................................................................................... 591 A.2 ENTROPY AND CONDITIONAL ENTROPY ............................................................ 595 A. 3 PROPERTIES OF ENTROPY ............................................................................... 606 B HYPERBOLIC MAPS AND INVARIANT MANIFOLDS ...................................................... 625 B. L THE CONTRACTION MAPPING PRINCIPLE ..................................................... 625 B.2 GENERALIZED EIGENSPACES ........................................................................628 B.3 THE SPECTRUM OF A LINEAR MAP .................................................................. 630 B.4 HYPERBOLIC LINEAR MAPS ............................................................................ 633 B.5 ADMISSIBLE MANIFOLDS: THE HADAMARD METHOD ......................................638 B.6 THE INCLINATION LEMMA AND HOMOCLINIC TANGLES .................................... 655 CONTENTS XIV B.7 ABSOLUTE CONTINUITY ...................................................................................659 HINTS AND ANSWERS TO THE EXERCISES ........................................................................... 671 BIBLIOGRAPHY ............................................................................................................679 INDEX OF PERSONS .........................................................................................................703 INDEX ............................................................................................................................ 707 INDEX OF THEOREMS ...................................................................................................... 721
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author	Fisher, Todd Hasselblatt, Boris 1961-
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indexdate	2024-12-20T19:23:29Z
institution	BVB
institution_GND	(DE-588)1066118477
isbn	9783037192009 3037192003
language	English
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open_access_boolean
owner	DE-19 DE-BY-UBM
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physical	xiv, 723 Seiten Illustrationen 24 cm x 17 cm
publishDate	2019
publishDateSearch	2019
publishDateSort	2019
publisher	European Mathematical Society
record_format	marc
series2	Zurich lectures in advanced mathematics
spellingShingle	Fisher, Todd Hasselblatt, Boris 1961- Hyperbolic flows Dynamisches System (DE-588)4013396-5 gnd Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd Hyperbolisches System (DE-588)4191897-6 gnd Ergodische Kette (DE-588)4402921-4 gnd
subject_GND	(DE-588)4013396-5 (DE-588)4496581-3 (DE-588)4191897-6 (DE-588)4402921-4
title	Hyperbolic flows
title_auth	Hyperbolic flows
title_exact_search	Hyperbolic flows
title_full	Hyperbolic flows Todd Fisher, Boris Hasselblatt
title_fullStr	Hyperbolic flows Todd Fisher, Boris Hasselblatt
title_full_unstemmed	Hyperbolic flows Todd Fisher, Boris Hasselblatt
title_short	Hyperbolic flows
title_sort	hyperbolic flows
topic	Dynamisches System (DE-588)4013396-5 gnd Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd Hyperbolisches System (DE-588)4191897-6 gnd Ergodische Kette (DE-588)4402921-4 gnd
topic_facet	Dynamisches System Hyperbolisches Differentialgleichungssystem Hyperbolisches System Ergodische Kette
url	http://digitale-objekte.hbz-nrw.de/storage2/2020/10/01/file_8/8922272.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032987005&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT fishertodd hyperbolicflows AT hasselblattboris hyperbolicflows AT europeanmathematicalsocietypublishinghouseethzentrumsewa27 hyperbolicflows

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