Nonuniform hyperbolicity: dynamics of systems with nonzero Lyapunov exponents
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Edition: | 1. publ. |
| Series: | Encyclopedia of mathematics and its applications
115 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIV, 513 S. graph. Darst. |
| ISBN: | 9780521832588 0521832586 |
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MARC
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| 100 | 1 | |a Barreira, Luis |d 1968- |e Verfasser |0 (DE-588)128529717 |4 aut | |
| 245 | 1 | 0 | |a Nonuniform hyperbolicity |b dynamics of systems with nonzero Lyapunov exponents |c Luis Barreira ; Yakov Pesin |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
| 300 | |a XIV, 513 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Encyclopedia of mathematics and its applications |v 115 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Sistemas dinâmicos |2 larpcal | |
| 650 | 4 | |a Lyapunov exponents | |
| 650 | 4 | |a Lyapunov stability | |
| 650 | 4 | |a Dynamics | |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ljapunov-Exponent |0 (DE-588)4123668-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hyperbolizität |0 (DE-588)4710615-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 0 | 1 | |a Hyperbolizität |0 (DE-588)4710615-3 |D s |
| 689 | 0 | 2 | |a Ljapunov-Exponent |0 (DE-588)4123668-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Pesin, Yakov B. |d 1946- |e Verfasser |0 (DE-588)129370533 |4 aut | |
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Record in the Search Index
| _version_ | 1804137244861136896 |
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| adam_text | ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS NONUNIFORM
HYPERBOLICITY DYNAMICS OF SYSTEMS WITH NONZERO LYAPUNOV EXPONENTS LUIS
BARREIRA INSTITUTO SUPERIOR TECNICO, LISBON YAKOV PESIN THE PENNSYLVANIA
STATE UNIVERSITY, UNIVERSITY PARK I CAMBRIDGE UNIVERSITY PRESS CONTENTS
PREFACE PAGE XIII INTRODUCTION 1 PART I LINEAR THEORY 1 THE CONCEPT OF
NONUNIFORM HYPERBOLICITY 9 1.1 MOTIVATION 9 1.2 BASIC SETTING 13 1.2.1
EXPONENTIAL SPLITTING AND NONUNIFORM HYPERBOLICITY 13 1.2.2 TEMPERED
EQUIVALENCE 14 1.2.3 THE CONTINUOUS-TIME CASE 15 1.3 LYAPUNOV EXPONENTS
ASSOCIATED TO SEQUENCES OF MATRICES 16 1.3.1 DEFINITION OF THE LYAPUNOV
EXPONENT 16 1.3.2 FORWARD AND BACKWARD REGULARITY 18 1.3.3 A CRITERION
OF FORWARD REGULARITY FOR TRIANGULAR MATRICES 25 1.3.4 THE
LYAPUNOV-PERRON REGULARITY 31 1.4 NOTES 33 2 LYAPUNOV EXPONENTS FOR
LINEAR EXTENSIONS 35 2.1 COCYCLES OVER DYNAMICAL SYSTEMS 35 2.1.1
COCYCLES AND LINEAR EXTENSIONS 35 2.1.2 COHOMOLOGY AND TEMPERED
EQUIVALENCE 37 2.1.3 EXAMPLES AND BASIC CONSTRUCTIONS 39 2.2
HYPERBOLICITY OF COCYCLES 41 2.2.1 HYPERBOLIC COCYCLES , 41 2.2.2
REGULAR SETS OF HYPERBOLIC COCYCLES 43 2.2.3 COCYCLES OVER TOPOLOGICAL
SPACES 46 2.3 LYAPUNOV EXPONENTS FOR COCYCLES 46 2.4 SPACES OF COCYCLES
50 VLL VIII CONTENTS 3 REGULARITY OF COCYCLES 53 3.1 THE LYAPUNOV-PERRON
REGULARITY 53 3.2 LYAPUNOV EXPONENTS AND BASIC CONSTRUCTIONS 57 3.3
LYAPUNOV EXPONENTS AND HYPERBOLICITY 59 3.4 THE MULTIPLICATIVE ERGODIC
THEOREM 64 3.4.1 ONE-DIMENSIONAL COCYCLES AND BIRKHOFF S ERGODIC THEOREM
64 3.4.2 OSELEDETS PROOF OF THE MULTIPLICATIVE ERGODIC THEOREM 65 3.4.3
LYAPUNOV EXPONENTS AND SUBADDITIVE ERGODIC THEOREM 69 3.4.4
RAGHUNATHAN S PROOF OF THE MULTIPLICATIVE ERGODIC THEOREM 70 3.5
TEMPERING KERNELS AND THE REDUCTION THEOREMS 75 3.5.1 LYAPUNOV INNER
PRODUCTS 76 3.5.2 THE OSELEDETS-PESIN REDUCTION THEOREM 77 3.5.3 A
TEMPERING KERNEL 80 3.5.4 ZIMMER S AMENABLE REDUCTION 82 3.5.5 THE CASE
OF NONINVERTIBLE COCYCLES 82 3.6 MORE RESULTS ON LYAPUNOV-PERRON
REGULARITY 83 3.6.1 HIGHER-RANK ABELIAN ACTIONS 83 3.6.2 THE CASE OF
FLOWS 88 3.6.3 NONPOSITIVELY CURVED SPACES 91 3.7 NOTES 94 4 METHODS FOR
ESTIMATING EXPONENTS 95 4.1 CONE AND LYAPUNOV FUNCTION TECHNIQUES 95
4.1.1 LYAPUNOV FUNCTIONS 96 4.1.2 A CRITERION FOR NONVANISHING LYAPUNOV
EXPONENTS 98 4.1.3 INVARIANT CONE FAMILIES 101 4.2 COCYCLES WITH VALUES
IN THE SYMPLECTIC GROUP 102 4.3 MONOTONE OPERATORS AND LYAPUNOV
EXPONENTS 106 4.3.1 THE ALGEBRA OF POTAPOV 106 4.3.2 LYAPUNOV EXPONENTS
FOR J-SEPARATED COCYCLES 108 4.3.3 THE LYAPUNOV SPECTRUM FOR CONFORMALLY
HAMILTONIAN SYSTEMS 112 4.4 A REMARK ON APPLICATIONS OF CONE TECHNIQUES
116 4.5 NOTES . . 117 5 THE DERIVATIVE COCYCLE 118 5.1 SMOOTH DYNAMICAL
SYSTEMS AND THE DERIVATIVE COCYCLE 118 5.2 NONUNIFORMLY HYPERBOLIC
DIFFEOMORPHISMS 119 5.3 HOLDER CONTINUITY OF INVARIANT DISTRIBUTIONS 122
5.4 LYAPUNOV EXPONENT AND REGULARITY OF THE DERIVATIVE COCYCLE 125 5.5
ON THE NOTION OF DYNAMICAL SYSTEMS WITH NONZERO LYAPUNOV EXPONENTS 129
CONTENTS IX 5.6 REGULAR NEIGHBORHOODS 130 5.7 COCYCLES OVER SMOOTH FLOWS
133 5.8 SEMICONTINUITY OF LYAPUNOV EXPONENTS 134 PART II EXAMPLES AND
FOUNDATIONS OF THE NONLINEAR THEORY 6 EXAMPLES OF SYSTEMS WITH
HYPERBOLIC BEHAVIOR 139 6.1 UNIFORMLY HYPERBOLIC SETS 139 6.1.1
HYPERBOLIC SETS FOR MAPS 139 6.1.2 HYPERBOLIC SETS FOR FLOWS 143 6.1.3
LINEAR HORSESHOES 144 6.1.4 NONLINEAR HORSESHOES 147 6.2 NONUNIFORMLY
HYPERBOLIC PERTURBATIONS OF HORSESHOES 152 6.2.1 SLOW EXPANSION NEAR A
FIXED POINT 152 6.2.2 FURTHER MODIFICATIONS 154 6.3 DIFFEOMORPHISMS WITH
NONZERO LYAPUNOV EXPONENTS ON SURFACES 158 6.3.1 ANALYTIC NONUNIFORMLY
HYPERBOLIC DIFFEOMORPHISMS 159 6.3.2 A NONUNIFORMLY HYPERBOLIC
DIFFEOMORPHISM ON THE SPHERE 163 6.3.3 NONUNIFORMLY HYPERBOLIC
DIFFEOMORPHISMS ON COMPACT SURFACES 164 6.3.4 A NONUNIFORMLY HYPERBOLIC
DIFFEOMORPHISM OF THE TORUS 166 6.4 PSEUDO-ANOSOV MAPS 167 6.4.1
DEFINITIONS AND BASIC PROPERTIES 168 6.4.2 SMOOTH MODELS OF
PSEUDO-ANOSOV MAPS 171 6.5 NONUNIFORMLY HYPERBOLIC FLOWS 182 6.6 SOME
OTHER EXAMPLES 185 6.7 NOTES 187 7 STABLE MANIFOLD THEORY 188 7.1 THE
STABLE MANIFOLD THEOREM 188 7.2 NONUNIFORMLY HYPERBOLIC SEQUENCES OF
DIFFEOMORPHISMS 191 7.3 THE HADAMARD-PERRON THEOREM: HADAMARD S METHOD
192 7.3.1 INVARIANT CONE FAMILIES 193 7.3.2 ADMISSIBLE MANIFOLDS 196
7.3.3 EXISTENCE OF (S, Y)- AND (W, Y)-MANIFOLDS 200 7.3.4 INVARIANT
FAMILIES OF LOCAL MANIFOLDS 203 7.3.5 HIGHER DIFFERENTIABILITY OF
INVARIANT MANIFOLDS 205 7.4 THE GRAPH TRANSFORM PROPERTY 206 7.5 THE
HADAMARD-PERRON THEOREM: PERRON S METHOD 207 7.5.1 AN ABSTRACT VERSION
OF THE STABLE MANIFOLD THEOREM 207 7.5.2 SMOOTHNESS OF LOCAL MANIFOLDS
215 7.6 LOCAL UNSTABLE MANIFOLDS 220 X CONTENTS 7.7 THE STABLE MANIFOLD
THEOREM FOR FLOWS 221 7.8 C 1 PATHOLOGICAL BEHAVIOR: PUGH S EXAMPLE 221
7.9 NOTES 225 8 BASIC PROPERTIES OF STABLE AND UNSTABLE MANIFOLDS 226
8.1 CHARACTERIZATION AND SIZES OF LOCAL STABLE MANIFOLDS 226 8.2 GLOBAL
STABLE AND UNSTABLE MANIFOLDS 229 8.3 FOLIATIONS WITH SMOOTH LEAVES 231
8.4 FILTRATIONS OF INTERMEDIATE LOCAL AND GLOBAL MANIFOLDS 232 8.5 THE
LIPSCHITZ PROPERTY OF INTERMEDIATE FOLIATIONS 236 8.6 THE ABSOLUTE
CONTINUITY PROPERTY 240 8.6.1 ABSOLUTE CONTINUITY OF HOLONOMY MAPS 242
8.6.2 ABSOLUTE CONTINUITY OF LOCAL STABLE MANIFOLDS 251 8.6.3 FOLIATION
THAT IS NOT ABSOLUTELY CONTINUOUS 254 8.6.4 THE JACOBIAN OF THE HOLONOMY
MAP 255 8.7 NOTES 257 PART III ERGODIC THEORY OF SMOOTH AND SRB MEASURES
9 SMOOTH MEASURES 261 9.1 ERGODIC COMPONENTS 261 9.2 LOCAL ERGODICITY
266 9.3 THE 5- AND U -MEASURES * 282 9.4 THE LEAF-SUBORDINATED PARTITION
AND THE /^-PROPERTY 285 9.5 THE BERNOULLI PROPERTY 290 9.6 THE
CONTINUOUS-TIME CASE 297 9.7 NOTES 303 10 MEASURE-THEORETIC ENTROPY AND
LYAPUNOV EXPONENTS 304 10.1 ENTROPY OF MEASURABLE TRANSFORMATIONS 3 04
10.2 THE MARGULIS-RUELLE INEQUALITY 305 10.3 THE TOPOLOGICAL ENTROPY AND
LYAPUNOV EXPONENTS 308 10.4 THE ENTROPY FORMULA 311 10.5 MANE S PROOF OF
THE ENTROPY FORMULA 315 10.6 NOTES 324 11 STABLE ERGODICITY AND LYAPUNOV
EXPONENTS. MORE EXAMPLES OF SYSTEMS WITH NONZERO EXPONENTS 32 6 11.1
UNIFORM PARTIAL HYPERBOLICITY AND STABLE ERGODICITY 326 11.2 PARTIALLY
HYPERBOLIC SYSTEMS WITH NONZERO LYAPUNOV EXPONENTS 329 11.3 HYPERBOLIC
DIFFEOMORPHISMS WITH COUNTABLY MANY ERGODIC COMPONENTS 337 11.4
EXISTENCE OF HYPERBOLIC DIFFEOMORPHISMS ON COMPACT MANIFOLDS 349 11.5
EXISTENCE OF HYPERBOLIC FLOWS ON COMPACT MANIFOLDS 369 11.6 FOLIATIONS
THAT ARE NOT ABSOLUTELY CONTINUOUS 378 CONTENTS XI 11.7 AN OPEN SET OF
DIFFEOMORPHISMS WITH NONZERO LYAPUNOV EXPONENTS ON TORI 382 11.8 NOTES
383 12 GEODESIC FLOWS 385 12.1 HYPERBOLICITY OF GEODESIC FLOWS 385 12.2
ERGODIC PROPERTIES OF GEODESIC FLOWS 394 12.3 ENTROPY OF GEODESIC FLOWS
404 12.4 TOPOLOGICAL PROPERTIES OF GEODESIC FLOWS 407 12.5 THE
TEICHMULLER GEODESIC FLOW 409 12.6 NOTES 415 13 SRB MEASURES 417 13.1
DEFINITION AND ERGODIC PROPERTIES OF SRB MEASURES 417 13.2 A
CHARACTERIZATION OF SRB MEASURES 421 13.3 CONSTRUCTIONS OF SRB MEASURES
423 13.4 NOTES 430 PART IV GENERAL HYPERBOLIC MEASURES 14 HYPERBOLIC
MEASURES: ENTROPY AND DIMENSION 433 14.1 POINTWISE DIMENSIONS AND THE
LEDRAPPIER-YOUNG ENTROPY FORMULA 433 14.1.1 LOCAL ENTROPIES 434 14.1.2
LEAF POINTWISE DIMENSIONS 438 14.1.3 THE LEDRAPPIER-YOUNG ENTROPY
FORMULA 449 14.2 LOCAL PRODUCT STRUCTURE OF HYPERBOLIC MEASURES 450 14.3
APPLICATIONS TO DIMENSION THEORY 461 14.4 NOTES 461 15 HYPERBOLIC
MEASURES: TOPOLOGICAL PROPERTIES 463 15.1 THE CLOSING LEMMA 463 15.2 THE
SHADOWING LEMMA 472 15.3 THE LIVSHITZ THEOREM 473 15.4 HYPERBOLIC
PERIODIC ORBITS 474 15.5 TOPOLOGICAL TRANSITIVITY AND SPECTRAL
DECOMPOSITION 482 15.6 ENTROPY, HORSESHOES, AND PERIODIC POINTS 482 15.7
CONTINUITY PROPERTIES OF ENTROPY 485 BIBLIOGRAPHY 491 INDEX 501
|
| adam_txt |
ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS NONUNIFORM
HYPERBOLICITY DYNAMICS OF SYSTEMS WITH NONZERO LYAPUNOV EXPONENTS LUIS
BARREIRA INSTITUTO SUPERIOR TECNICO, LISBON YAKOV PESIN THE PENNSYLVANIA
STATE UNIVERSITY, UNIVERSITY PARK I CAMBRIDGE UNIVERSITY PRESS CONTENTS
PREFACE PAGE XIII INTRODUCTION 1 PART I LINEAR THEORY 1 THE CONCEPT OF
NONUNIFORM HYPERBOLICITY 9 1.1 MOTIVATION 9 1.2 BASIC SETTING 13 1.2.1
EXPONENTIAL SPLITTING AND NONUNIFORM HYPERBOLICITY 13 1.2.2 TEMPERED
EQUIVALENCE 14 1.2.3 THE CONTINUOUS-TIME CASE 15 1.3 LYAPUNOV EXPONENTS
ASSOCIATED TO SEQUENCES OF MATRICES 16 1.3.1 DEFINITION OF THE LYAPUNOV
EXPONENT 16 1.3.2 FORWARD AND BACKWARD REGULARITY 18 1.3.3 A CRITERION
OF FORWARD REGULARITY FOR TRIANGULAR MATRICES 25 1.3.4 THE
LYAPUNOV-PERRON REGULARITY 31 1.4 NOTES 33 2 LYAPUNOV EXPONENTS FOR
LINEAR EXTENSIONS 35 2.1 COCYCLES OVER DYNAMICAL SYSTEMS 35 2.1.1
COCYCLES AND LINEAR EXTENSIONS 35 2.1.2 COHOMOLOGY AND TEMPERED
EQUIVALENCE 37 2.1.3 EXAMPLES AND BASIC CONSTRUCTIONS 39 2.2
HYPERBOLICITY OF COCYCLES 41 2.2.1 HYPERBOLIC COCYCLES , 41 2.2.2
REGULAR SETS OF HYPERBOLIC COCYCLES 43 2.2.3 COCYCLES OVER TOPOLOGICAL
SPACES 46 2.3 LYAPUNOV EXPONENTS FOR COCYCLES 46 2.4 SPACES OF COCYCLES
50 VLL VIII CONTENTS 3 REGULARITY OF COCYCLES 53 3.1 THE LYAPUNOV-PERRON
REGULARITY 53 3.2 LYAPUNOV EXPONENTS AND BASIC CONSTRUCTIONS 57 3.3
LYAPUNOV EXPONENTS AND HYPERBOLICITY 59 3.4 THE MULTIPLICATIVE ERGODIC
THEOREM 64 3.4.1 ONE-DIMENSIONAL COCYCLES AND BIRKHOFF'S ERGODIC THEOREM
64 3.4.2 OSELEDETS' PROOF OF THE MULTIPLICATIVE ERGODIC THEOREM 65 3.4.3
LYAPUNOV EXPONENTS AND SUBADDITIVE ERGODIC THEOREM 69 3.4.4
RAGHUNATHAN'S PROOF OF THE MULTIPLICATIVE ERGODIC THEOREM 70 3.5
TEMPERING KERNELS AND THE REDUCTION THEOREMS 75 3.5.1 LYAPUNOV INNER
PRODUCTS 76 3.5.2 THE OSELEDETS-PESIN REDUCTION THEOREM 77 3.5.3 A
TEMPERING KERNEL 80 3.5.4 ZIMMER'S AMENABLE REDUCTION 82 3.5.5 THE CASE
OF NONINVERTIBLE COCYCLES 82 3.6 MORE RESULTS ON LYAPUNOV-PERRON
REGULARITY 83 3.6.1 HIGHER-RANK ABELIAN ACTIONS 83 3.6.2 THE CASE OF
FLOWS 88 3.6.3 NONPOSITIVELY CURVED SPACES 91 3.7 NOTES 94 4 METHODS FOR
ESTIMATING EXPONENTS 95 4.1 CONE AND LYAPUNOV FUNCTION TECHNIQUES 95
4.1.1 LYAPUNOV FUNCTIONS 96 4.1.2 A CRITERION FOR NONVANISHING LYAPUNOV
EXPONENTS 98 4.1.3 INVARIANT CONE FAMILIES 101 4.2 COCYCLES WITH VALUES
IN THE SYMPLECTIC GROUP 102 4.3 MONOTONE OPERATORS AND LYAPUNOV
EXPONENTS 106 4.3.1 THE ALGEBRA OF POTAPOV 106 4.3.2 LYAPUNOV EXPONENTS
FOR J-SEPARATED COCYCLES 108 4.3.3 THE LYAPUNOV SPECTRUM FOR CONFORMALLY
HAMILTONIAN SYSTEMS 112 4.4 A REMARK ON APPLICATIONS OF CONE TECHNIQUES
116 4.5 NOTES . . 117 5 THE DERIVATIVE COCYCLE 118 5.1 SMOOTH DYNAMICAL
SYSTEMS AND THE DERIVATIVE COCYCLE 118 5.2 NONUNIFORMLY HYPERBOLIC
DIFFEOMORPHISMS 119 5.3 HOLDER CONTINUITY OF INVARIANT DISTRIBUTIONS 122
5.4 LYAPUNOV EXPONENT AND REGULARITY OF THE DERIVATIVE COCYCLE 125 5.5
ON THE NOTION OF DYNAMICAL SYSTEMS WITH NONZERO LYAPUNOV EXPONENTS 129
CONTENTS IX 5.6 REGULAR NEIGHBORHOODS 130 5.7 COCYCLES OVER SMOOTH FLOWS
133 5.8 SEMICONTINUITY OF LYAPUNOV EXPONENTS 134 PART II EXAMPLES AND
FOUNDATIONS OF THE NONLINEAR THEORY 6 EXAMPLES OF SYSTEMS WITH
HYPERBOLIC BEHAVIOR 139 6.1 UNIFORMLY HYPERBOLIC SETS 139 6.1.1
HYPERBOLIC SETS FOR MAPS 139 6.1.2 HYPERBOLIC SETS FOR FLOWS 143 6.1.3
LINEAR HORSESHOES 144 6.1.4 NONLINEAR HORSESHOES 147 6.2 NONUNIFORMLY
HYPERBOLIC PERTURBATIONS OF HORSESHOES 152 6.2.1 SLOW EXPANSION NEAR A
FIXED POINT 152 6.2.2 FURTHER MODIFICATIONS 154 6.3 DIFFEOMORPHISMS WITH
NONZERO LYAPUNOV EXPONENTS ON SURFACES 158 6.3.1 ANALYTIC NONUNIFORMLY
HYPERBOLIC DIFFEOMORPHISMS 159 6.3.2 A NONUNIFORMLY HYPERBOLIC
DIFFEOMORPHISM ON THE SPHERE 163 6.3.3 NONUNIFORMLY HYPERBOLIC
DIFFEOMORPHISMS ON COMPACT SURFACES 164 6.3.4 A NONUNIFORMLY HYPERBOLIC
DIFFEOMORPHISM OF THE TORUS 166 6.4 PSEUDO-ANOSOV MAPS " 167 6.4.1
DEFINITIONS AND BASIC PROPERTIES 168 6.4.2 SMOOTH MODELS OF
PSEUDO-ANOSOV MAPS 171 6.5 NONUNIFORMLY HYPERBOLIC FLOWS 182 6.6 SOME
OTHER EXAMPLES 185 6.7 NOTES 187 7 STABLE MANIFOLD THEORY 188 7.1 THE
STABLE MANIFOLD THEOREM 188 7.2 NONUNIFORMLY HYPERBOLIC SEQUENCES OF
DIFFEOMORPHISMS 191 7.3 THE HADAMARD-PERRON THEOREM: HADAMARD'S METHOD
192 7.3.1 INVARIANT CONE FAMILIES 193 7.3.2 ADMISSIBLE MANIFOLDS 196
7.3.3 EXISTENCE OF (S, Y)- AND (W, Y)-MANIFOLDS 200 7.3.4 INVARIANT
FAMILIES OF LOCAL MANIFOLDS 203 7.3.5 HIGHER DIFFERENTIABILITY OF
INVARIANT MANIFOLDS 205 7.4 THE GRAPH TRANSFORM PROPERTY 206 7.5 THE
HADAMARD-PERRON THEOREM: PERRON'S METHOD 207 7.5.1 AN ABSTRACT VERSION
OF THE STABLE MANIFOLD THEOREM 207 7.5.2 SMOOTHNESS OF LOCAL MANIFOLDS '
215 7.6 LOCAL UNSTABLE MANIFOLDS 220 X CONTENTS 7.7 THE STABLE MANIFOLD
THEOREM FOR FLOWS 221 7.8 C 1 PATHOLOGICAL BEHAVIOR: PUGH'S EXAMPLE 221
7.9 NOTES 225 8 BASIC PROPERTIES OF STABLE AND UNSTABLE MANIFOLDS 226
8.1 CHARACTERIZATION AND SIZES OF LOCAL STABLE MANIFOLDS 226 8.2 GLOBAL
STABLE AND UNSTABLE MANIFOLDS 229 8.3 FOLIATIONS WITH SMOOTH LEAVES 231
8.4 FILTRATIONS OF INTERMEDIATE LOCAL AND GLOBAL MANIFOLDS 232 8.5 THE
LIPSCHITZ PROPERTY OF INTERMEDIATE FOLIATIONS 236 8.6 THE ABSOLUTE
CONTINUITY PROPERTY 240 8.6.1 ABSOLUTE CONTINUITY OF HOLONOMY MAPS 242
8.6.2 ABSOLUTE CONTINUITY OF LOCAL STABLE MANIFOLDS 251 8.6.3 FOLIATION
THAT IS NOT ABSOLUTELY CONTINUOUS 254 8.6.4 THE JACOBIAN OF THE HOLONOMY
MAP 255 8.7 NOTES 257 PART III ERGODIC THEORY OF SMOOTH AND SRB MEASURES
9 SMOOTH MEASURES 261 9.1 ERGODIC COMPONENTS 261 9.2 LOCAL ERGODICITY
266 9.3 THE 5- AND U -MEASURES * 282 9.4 THE LEAF-SUBORDINATED PARTITION
AND THE /^-PROPERTY 285 9.5 THE BERNOULLI PROPERTY 290 9.6 THE
CONTINUOUS-TIME CASE 297 9.7 NOTES 303 10 MEASURE-THEORETIC ENTROPY AND
LYAPUNOV EXPONENTS 304 10.1 ENTROPY OF MEASURABLE TRANSFORMATIONS 3 04
10.2 THE MARGULIS-RUELLE INEQUALITY 305 10.3 THE TOPOLOGICAL ENTROPY AND
LYAPUNOV EXPONENTS 308 10.4 THE ENTROPY FORMULA 311 10.5 MANE'S PROOF OF
THE ENTROPY FORMULA 315 10.6 NOTES 324 11 STABLE ERGODICITY AND LYAPUNOV
EXPONENTS. MORE EXAMPLES OF SYSTEMS WITH NONZERO EXPONENTS 32 6 11.1
UNIFORM PARTIAL HYPERBOLICITY AND STABLE ERGODICITY 326 11.2 PARTIALLY
HYPERBOLIC SYSTEMS WITH NONZERO LYAPUNOV EXPONENTS 329 11.3 HYPERBOLIC
DIFFEOMORPHISMS WITH COUNTABLY MANY ERGODIC COMPONENTS 337 11.4
EXISTENCE OF HYPERBOLIC DIFFEOMORPHISMS ON COMPACT MANIFOLDS 349 11.5
EXISTENCE OF HYPERBOLIC FLOWS ON COMPACT MANIFOLDS 369 11.6 FOLIATIONS
THAT ARE NOT ABSOLUTELY CONTINUOUS 378 CONTENTS XI 11.7 AN OPEN SET OF
DIFFEOMORPHISMS WITH NONZERO LYAPUNOV EXPONENTS ON TORI 382 11.8 NOTES
383 12 GEODESIC FLOWS 385 12.1 HYPERBOLICITY OF GEODESIC FLOWS 385 12.2
ERGODIC PROPERTIES OF GEODESIC FLOWS 394 12.3 ENTROPY OF GEODESIC FLOWS
404 12.4 TOPOLOGICAL PROPERTIES OF GEODESIC FLOWS 407 12.5 THE
TEICHMULLER GEODESIC FLOW 409 12.6 NOTES 415 13 SRB MEASURES 417 13.1
DEFINITION AND ERGODIC PROPERTIES OF SRB MEASURES 417 13.2 A
CHARACTERIZATION OF SRB MEASURES 421 13.3 CONSTRUCTIONS OF SRB MEASURES
423 13.4 NOTES 430 PART IV GENERAL HYPERBOLIC MEASURES 14 HYPERBOLIC
MEASURES: ENTROPY AND DIMENSION 433 14.1 POINTWISE DIMENSIONS AND THE
LEDRAPPIER-YOUNG ENTROPY FORMULA 433 14.1.1 LOCAL ENTROPIES 434 14.1.2
LEAF POINTWISE DIMENSIONS 438 14.1.3 THE LEDRAPPIER-YOUNG ENTROPY
FORMULA 449 14.2 LOCAL PRODUCT STRUCTURE OF HYPERBOLIC MEASURES 450 14.3
APPLICATIONS TO DIMENSION THEORY 461 14.4 NOTES 461 15 HYPERBOLIC
MEASURES: TOPOLOGICAL PROPERTIES 463 15.1 THE CLOSING LEMMA 463 15.2 THE
SHADOWING LEMMA 472 15.3 THE LIVSHITZ THEOREM 473 15.4 HYPERBOLIC
PERIODIC ORBITS 474 15.5 TOPOLOGICAL TRANSITIVITY AND SPECTRAL
DECOMPOSITION 482 15.6 ENTROPY, HORSESHOES, AND PERIODIC POINTS 482 15.7
CONTINUITY PROPERTIES OF ENTROPY 485 BIBLIOGRAPHY 491 INDEX 501 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Barreira, Luis 1968- Pesin, Yakov B. 1946- |
| author_GND | (DE-588)128529717 (DE-588)129370533 |
| author_facet | Barreira, Luis 1968- Pesin, Yakov B. 1946- |
| author_role | aut aut |
| author_sort | Barreira, Luis 1968- |
| author_variant | l b lb y b p yb ybp |
| building | Verbundindex |
| bvnumber | BV023023827 |
| callnumber-first | Q - Science |
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| callnumber-sort | QA 3871 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 810 |
| classification_tum | MAT 587f |
| ctrlnum | (OCoLC)122261902 (DE-599)BSZ273717235 |
| dewey-full | 531/.11 |
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| dewey-raw | 531/.11 |
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| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV023023827 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:14:14Z |
| indexdate | 2024-07-09T21:09:13Z |
| institution | BVB |
| isbn | 9780521832588 0521832586 |
| language | English |
| lccn | 2007013057 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016227835 |
| oclc_num | 122261902 |
| open_access_boolean | |
| owner | DE-29T DE-703 DE-83 DE-11 DE-188 DE-91G DE-BY-TUM |
| owner_facet | DE-29T DE-703 DE-83 DE-11 DE-188 DE-91G DE-BY-TUM |
| physical | XIV, 513 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Barreira, Luis 1968- Verfasser (DE-588)128529717 aut Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents Luis Barreira ; Yakov Pesin 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 XIV, 513 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 115 Includes bibliographical references and index Sistemas dinâmicos larpcal Lyapunov exponents Lyapunov stability Dynamics Dynamisches System (DE-588)4013396-5 gnd rswk-swf Ljapunov-Exponent (DE-588)4123668-3 gnd rswk-swf Hyperbolizität (DE-588)4710615-3 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Hyperbolizität (DE-588)4710615-3 s Ljapunov-Exponent (DE-588)4123668-3 s DE-604 Pesin, Yakov B. 1946- Verfasser (DE-588)129370533 aut Encyclopedia of mathematics and its applications 115 (DE-604)BV000903719 115 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016227835&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barreira, Luis 1968- Pesin, Yakov B. 1946- Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents Encyclopedia of mathematics and its applications Sistemas dinâmicos larpcal Lyapunov exponents Lyapunov stability Dynamics Dynamisches System (DE-588)4013396-5 gnd Ljapunov-Exponent (DE-588)4123668-3 gnd Hyperbolizität (DE-588)4710615-3 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4123668-3 (DE-588)4710615-3 |
| title | Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents |
| title_auth | Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents |
| title_exact_search | Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents |
| title_exact_search_txtP | Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents |
| title_full | Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents Luis Barreira ; Yakov Pesin |
| title_fullStr | Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents Luis Barreira ; Yakov Pesin |
| title_full_unstemmed | Nonuniform hyperbolicity dynamics of systems with nonzero Lyapunov exponents Luis Barreira ; Yakov Pesin |
| title_short | Nonuniform hyperbolicity |
| title_sort | nonuniform hyperbolicity dynamics of systems with nonzero lyapunov exponents |
| title_sub | dynamics of systems with nonzero Lyapunov exponents |
| topic | Sistemas dinâmicos larpcal Lyapunov exponents Lyapunov stability Dynamics Dynamisches System (DE-588)4013396-5 gnd Ljapunov-Exponent (DE-588)4123668-3 gnd Hyperbolizität (DE-588)4710615-3 gnd |
| topic_facet | Sistemas dinâmicos Lyapunov exponents Lyapunov stability Dynamics Dynamisches System Ljapunov-Exponent Hyperbolizität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016227835&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT barreiraluis nonuniformhyperbolicitydynamicsofsystemswithnonzerolyapunovexponents AT pesinyakovb nonuniformhyperbolicitydynamicsofsystemswithnonzerolyapunovexponents |