Lectures on ergodic theory and Pesin theory on compact manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1993
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| Ausgabe: | 1. publ. |
| Schriftenreihe: | London Mathematical Society: London Mathematical Society lecture note series
180 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 162 S. graph. Darst. |
| ISBN: | 0521435935 |
Internformat
MARC
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| 100 | 1 | |a Pollicott, Mark |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lectures on ergodic theory and Pesin theory on compact manifolds |c Mark Pollicott |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1993 | |
| 300 | |a IX, 162 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Introduction 1
Part I. The basic theory
Chapter 1. Invariant measures and some ergodic theory 5
1.1 Invariant measures, 5
1.2 Poincare recurrence, 9
1.3 Ergodic measures, 9
1.4 Ergodic decomposition, 10
1.5 The ergodic theorem, 12
1.6 Proof of the ergodic theorem, 15
1.7 Proof of the ergodic decomposition lemma, 18
Notes. 19
Chapter 2. Ergodic theory for manifolds and Liapunov exponents 21
2.1 The subadditive ergodic theorem, 21
2.2 The subadditive ergodic theorem and diffeomorphisms, 22
2.3 Oseledec type theorems, 23
2.4 Some examples, 25
2.5 Proof of the Oseledec theorem, 31
2.6 Further refinements of the Oseledec theorem, 36
2.7 Proof of the subadditive ergodic theorem, 37
Notes. 40
Chapter 3. Entropy 43
3.1 Measure theoretic entropy, 43
3.2 Measure theoretic entropy and Liapunov exponents, 46
3.3 Topological entropy, 48
3.4 Topological entropy and Liapunov exponents, 50
3.5 Equivalent definitions of measure theoretic entropy, 53
3.6 Proof of the Pesin Ruelle inequality, 58
3.7 Osceledec s theorem, topological entropy and Lie theory, 60
Notes. 62
(viii)
Chapter 4. The Pesin set and its structure 63
4.1 The Pesin set, 64
4.2 The Pesin set and Liapunov exponents, 68
4.3 Liapunov metrics on the Pesin set, 69
4.4 Local distortion, 71
4.5 Proofs of Propositions 4.1 and 4.2, 73
4.6 Liapunov exponents with the same sign, 76
Notes. 77
An interlude 79
(a) Some topical examples, 79
(b) Uniformly hyperbolic diffeomorphisms:
(i) Shadowing, (ii) Closing lemma, (iii) Stable manifolds, 83
Notes. 85
Part II. The applications
Chapter 5. Closing lemmas and periodic points 87
5.1 Liapunov neighborhoods, 87
5.2 Shadowing lemma, 90
5.3 Uniqueness of the shadowing point, 94
5.4 Closing lemmas, 95
5.5 An application of the closing lemma, 96
Notes. 98
Chapter 6. Structure of chaotic diffeomorphisms 99
6.1 The distribution of periodic points, 99
6.2 The number of periodic points, 101
6.3 Homoclinic points, 103
6.4 Generalized Smale horse shoes, 105
6.5 Entropy stability, 108
6.6 Entropy, volume growth and Yomdin s inequality, 110
6.7 Examples of discontinuity of entropy, 115
6.8 Proofs of propositions 6.1 and 6.2, 119
Notes. 122
(ix)
Chapter 7. Stable manifolds and more measure theory 123
7.1 Stable and unstable manifolds, 123
7.2 Equality in the Pesin Ruelle inequality, 127
7.3 Foliations and absolute continuity, 129
7.4 Ergodic components, 132
7.5 Proof of stable manifold theorem, 133
7.6 Ergodic components and absolute continuity, 137
Notes. 137
Appendix A. Some preliminary measure theory 139
Appendix B. Some preliminary differential geometry 145
Appendix G. Geodesic flows 151
References 155
|
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| id | DE-604.BV008043072 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:13:23Z |
| institution | BVB |
| isbn | 0521435935 |
| language | English |
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| physical | IX, 162 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Cambridge Univ. Press |
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| series | London Mathematical Society: London Mathematical Society lecture note series |
| series2 | London Mathematical Society: London Mathematical Society lecture note series |
| spelling | Pollicott, Mark Verfasser aut Lectures on ergodic theory and Pesin theory on compact manifolds Mark Pollicott 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1993 IX, 162 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society lecture note series 180 Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Diffeomorphismus (DE-588)4149767-3 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s Diffeomorphismus (DE-588)4149767-3 s DE-604 London Mathematical Society: London Mathematical Society lecture note series 180 (DE-604)BV000000130 180 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005291952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pollicott, Mark Lectures on ergodic theory and Pesin theory on compact manifolds London Mathematical Society: London Mathematical Society lecture note series Ergodentheorie (DE-588)4015246-7 gnd Diffeomorphismus (DE-588)4149767-3 gnd |
| subject_GND | (DE-588)4015246-7 (DE-588)4149767-3 |
| title | Lectures on ergodic theory and Pesin theory on compact manifolds |
| title_auth | Lectures on ergodic theory and Pesin theory on compact manifolds |
| title_exact_search | Lectures on ergodic theory and Pesin theory on compact manifolds |
| title_full | Lectures on ergodic theory and Pesin theory on compact manifolds Mark Pollicott |
| title_fullStr | Lectures on ergodic theory and Pesin theory on compact manifolds Mark Pollicott |
| title_full_unstemmed | Lectures on ergodic theory and Pesin theory on compact manifolds Mark Pollicott |
| title_short | Lectures on ergodic theory and Pesin theory on compact manifolds |
| title_sort | lectures on ergodic theory and pesin theory on compact manifolds |
| topic | Ergodentheorie (DE-588)4015246-7 gnd Diffeomorphismus (DE-588)4149767-3 gnd |
| topic_facet | Ergodentheorie Diffeomorphismus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005291952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
| work_keys_str_mv | AT pollicottmark lecturesonergodictheoryandpesintheoryoncompactmanifolds |