Lyapunov exponents and smooth ergodic theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2002]
|
| Schriftenreihe: | University lecture series
Volume 23 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 151 Seiten Diagramme |
| ISBN: | 0821829211 9780821829219 |
Internformat
MARC
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| 100 | 1 | |a Barreira, Luis |d 1968- |e Verfasser |0 (DE-588)128529717 |4 aut | |
| 245 | 1 | 0 | |a Lyapunov exponents and smooth ergodic theory |c Luis Barreira ; Yakov B. Pesin |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2002] | |
| 264 | 4 | |c © 2002 | |
| 300 | |a xii, 151 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a University lecture series |v Volume 23 | |
| 650 | 7 | |a Dynamische systemen |2 gtt | |
| 650 | 7 | |a Ergodiciteit |2 gtt | |
| 650 | 4 | |a Liapounov, Exposants de | |
| 650 | 4 | |a Théorie ergodique | |
| 650 | 4 | |a Ergodic theory | |
| 650 | 4 | |a Lyapunov exponents | |
| 650 | 0 | 7 | |a Ergodentheorie |0 (DE-588)4015246-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ljapunov-Exponent |0 (DE-588)4123668-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Ergodentheorie |0 (DE-588)4015246-7 |D s |
| 689 | 0 | 1 | |a Ljapunov-Exponent |0 (DE-588)4123668-3 |D s |
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| 700 | 1 | |a Pesin, Yakov B. |d 1946- |e Verfasser |0 (DE-588)129370533 |4 aut | |
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| 830 | 0 | |a University lecture series |v Volume 23 |w (DE-604)BV004153846 |9 23 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009733184 | ||
Datensatz im Suchindex
| _version_ | 1804129079080779776 |
|---|---|
| adam_text | Contents
Preface xi
Introduction 1
Chapter 1. Lyapunov Stability Theory of Differential Equations 5
1.1. Lyapunov Exponents for Differential Equations 6
1.2. Abstract Theory of Lyapunov Exponents 9
1.3. Forward and Backward Regularity 16
1.4. Stability Theory of Nonautonomous Differential Equations 26
1.5. Lyapunov Regularity and the Oseledets Decomposition 31
Chapter 2. Elements of Nonuniform Hyperbolic Theory 35
2.1. Dynamical Systems with Nonzero Lyapunov Exponents 36
2.2. Nonuniform Hyperbolicity and Regular Sets 45
2.3. Holder Continuity of Invariant Distributions 48
2.4. Proof of the Multiplicative Ergodic Theorem 51
Chapter 3. Examples of Nonuniformly Hyperbolic Systems 61
3.1. Anosov Diffeomorphisms 61
3.2. Diffeomorphisms with Nonzero Lyapunov Exponents on
Surfaces 66
3.3. A Flow with Nonzero Lyapunov Exponents 71
3.4. Geodesic Flows on Compact Manifolds of Nonpositive
Curvature 74
Chapter 4. Local Manifold Theory 81
4.1. Existence of Local Stable Manifolds 81
4.2. Basic Properties of Stable and Unstable Manifolds 94
4.3. Absolute Continuity Property 99
4.4. Computing the Jacobian of the Holonomy Map 109
4.5. Partial Hyperbolicity 111
Chapter 5. Ergodic Properties of Smooth Hyperbolic Measures 115
5.1. Absolute Continuity and Smooth Invariant Measures 115
5.2. Ergodicity of Smooth Hyperbolic Measures 117
5.3. Local Ergodicity 122
x CONTENTS
5.4. The Entropy Formula 130
5.5. SRB Measures and General Hyperbolic Measures 138
5.6. Geodesic Flows on Compact Surfaces of Nonpositive
Curvature 140
Bibliography 145
Index 147
|
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| author | Barreira, Luis 1968- Pesin, Yakov B. 1946- |
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| classification_rvk | SI 165 SK 810 |
| ctrlnum | (OCoLC)47838139 (DE-599)BVBBV014198563 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.42 |
| dewey-search | 515/.42 |
| dewey-sort | 3515 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014198563 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:59:26Z |
| institution | BVB |
| isbn | 0821829211 9780821829219 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009733184 |
| oclc_num | 47838139 |
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| physical | xii, 151 Seiten Diagramme |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | American Mathematical Society |
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| series | University lecture series |
| series2 | University lecture series |
| spelling | Barreira, Luis 1968- Verfasser (DE-588)128529717 aut Lyapunov exponents and smooth ergodic theory Luis Barreira ; Yakov B. Pesin Providence, Rhode Island American Mathematical Society [2002] © 2002 xii, 151 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 23 Dynamische systemen gtt Ergodiciteit gtt Liapounov, Exposants de Théorie ergodique Ergodic theory Lyapunov exponents Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Ljapunov-Exponent (DE-588)4123668-3 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s Ljapunov-Exponent (DE-588)4123668-3 s DE-604 Pesin, Yakov B. 1946- Verfasser (DE-588)129370533 aut Erscheint auch als Online-Ausgabe 978-1-4704-2170-0 University lecture series Volume 23 (DE-604)BV004153846 23 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009733184&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barreira, Luis 1968- Pesin, Yakov B. 1946- Lyapunov exponents and smooth ergodic theory University lecture series Dynamische systemen gtt Ergodiciteit gtt Liapounov, Exposants de Théorie ergodique Ergodic theory Lyapunov exponents Ergodentheorie (DE-588)4015246-7 gnd Ljapunov-Exponent (DE-588)4123668-3 gnd |
| subject_GND | (DE-588)4015246-7 (DE-588)4123668-3 |
| title | Lyapunov exponents and smooth ergodic theory |
| title_auth | Lyapunov exponents and smooth ergodic theory |
| title_exact_search | Lyapunov exponents and smooth ergodic theory |
| title_full | Lyapunov exponents and smooth ergodic theory Luis Barreira ; Yakov B. Pesin |
| title_fullStr | Lyapunov exponents and smooth ergodic theory Luis Barreira ; Yakov B. Pesin |
| title_full_unstemmed | Lyapunov exponents and smooth ergodic theory Luis Barreira ; Yakov B. Pesin |
| title_short | Lyapunov exponents and smooth ergodic theory |
| title_sort | lyapunov exponents and smooth ergodic theory |
| topic | Dynamische systemen gtt Ergodiciteit gtt Liapounov, Exposants de Théorie ergodique Ergodic theory Lyapunov exponents Ergodentheorie (DE-588)4015246-7 gnd Ljapunov-Exponent (DE-588)4123668-3 gnd |
| topic_facet | Dynamische systemen Ergodiciteit Liapounov, Exposants de Théorie ergodique Ergodic theory Lyapunov exponents Ergodentheorie Ljapunov-Exponent |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009733184&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
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