Smooth ergodic theory of random dynamical systems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1995
|
| Series: | Lecture notes in mathematics
1606 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 221 S. |
| ISBN: | 3540600043 0387600043 |
Staff View
MARC
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| 245 | 1 | 0 | |a Smooth ergodic theory of random dynamical systems |c Pei-Dong Liu ; Min Qian |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1995 | |
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Record in the Search Index
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| adam_text | Table of Contents
Introduction vii
Chapter 0. Preliminaries 1
§ 1. Measure Theory 1
§2. Measurable Partitions 5
§3. Conditional Entropies of Measurable Partitions 7
§4. Conditional Entropies of Measure Preserving Transformations: I 9
§5. Conditional Entropies of Measure Preserving Transformations: II.... 16
Chapter I. Entropy and Lyapunov Exponents of Random Diffeomorphisms . 22
§1. The Basic Measure Spaces and Invariant Measures 22
§2. Measure Theoretic Entropies of Random Diffeomorphisms 31
§3. Lyapunov Exponents of Random Diffeomorphisms 37
Chapter II. Estimation of Entropy from Above Through Lyapunov
Exponents 45
§ 1. Preliminaries 45
§2. Proof of Theorem 0.1 51
Chapter III. Stable Invariant Manifolds of Random Diffeomorphisms 55
§ 1. Some Preliminary Lemmas 55
§2. Some Technical Facts About Contracting Maps 61
§3. Local and Global Stable Manifolds 63
§4. Holder Continuity of Subbundles 73
§5. Absolute Continuity of Families of Submanifolds 84
§6. Absolute Continuity of Conditional Measures 86
Chapter IV. Estimation of Entropy from Below Through Lyapunov
Exponents 91
§1. Introduction and Formulation of the Main Result 91
§2. Construction of A Measurable Partition 93
§3. Estimation of the Entropy from Below 103
Chapter V. Stochastic Flows of Diffeomorphisms 109
§1. Preliminaries 109
§2. Lyapunov Exponents and Stable Manifolds of Stochastic Flows
of Diffeomorphisms 118
§3. Entropy of Stochastic Flows of Diffeomorphisms 124
Chapter VI. Characterization of Measures Satisfying Entropy Formula .... 128
§1. Basic Concepts and Formulation of the Main Result 129
§2. SBR Sample Measures: Sufficiency for Entropy Formula 137
§3. Lyapunov Charts 141
v
§4. Local Unstable Manifolds and Center Unstable Sets 146
§5. Related Measurable Partitions 154
§6. Some Consequences of Besicovitch s Covering Theorem 166
§7. The Main Proposition 170
§8. SBR Sample Measures: Necessity for Entropy Formula 175
Chapter VII. Random Perturbations of Hyperbolic Attractors 182
§1. Definitions and Statements of Results 183
§2. Technical Preparations for the Proof of the Main Result 192
§3. Proof of the Main Result 197
Appendix. A Margulis Ruelle Inequality for Random Dynamical Systems .. 207
§ 1. Notions and Preliminary Results 207
§2. The Main Result and It s Proof 209
References 216
Subject Index 219
vi
|
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| isbn | 3540600043 0387600043 |
| language | English |
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| physical | XI, 221 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| series2 | Lecture notes in mathematics |
| spelling | Liu, Pei-Dong Verfasser aut Smooth ergodic theory of random dynamical systems Pei-Dong Liu ; Min Qian Berlin [u.a.] Springer 1995 XI, 221 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1606 Ergodic theory Random dynamical systems Stochastic differential equations Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s DE-604 Differenzierbares dynamisches System (DE-588)4137931-7 s Qian, Min Verfasser aut Lecture notes in mathematics 1606 (DE-604)BV000676446 1606 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006848239&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liu, Pei-Dong Qian, Min Smooth ergodic theory of random dynamical systems Lecture notes in mathematics Ergodic theory Random dynamical systems Stochastic differential equations Ergodentheorie (DE-588)4015246-7 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4015246-7 (DE-588)4137931-7 |
| title | Smooth ergodic theory of random dynamical systems |
| title_auth | Smooth ergodic theory of random dynamical systems |
| title_exact_search | Smooth ergodic theory of random dynamical systems |
| title_full | Smooth ergodic theory of random dynamical systems Pei-Dong Liu ; Min Qian |
| title_fullStr | Smooth ergodic theory of random dynamical systems Pei-Dong Liu ; Min Qian |
| title_full_unstemmed | Smooth ergodic theory of random dynamical systems Pei-Dong Liu ; Min Qian |
| title_short | Smooth ergodic theory of random dynamical systems |
| title_sort | smooth ergodic theory of random dynamical systems |
| topic | Ergodic theory Random dynamical systems Stochastic differential equations Ergodentheorie (DE-588)4015246-7 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Ergodic theory Random dynamical systems Stochastic differential equations Ergodentheorie Differenzierbares dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006848239&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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