Introduction to smooth ergodic theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Soc.
2013
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| Schriftenreihe: | Graduate studies in mathematics
148 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 277 S. 26 cm |
| ISBN: | 9780821898536 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Titel: Introduction to smooth ergodic theory
Autor: Barreira, Luis
Jahr: 2013
Contents Preface vii Part 1. The Core of the Theory Chapter 1. Examples of Hyperbolic Dynamical Systems 3 §1.1. Anosov diffeomorphisms 4 §1.2. Anosov flows 8 §1.3. The Katok map of the 2-torus 13 §1.4. Diffeomorphisms with nonzero Lyapunov exponents on surfaces 23 §1.5. A flow with nonzero Lyapunov exponents , 27 Chapter 2. General Theory of Lyapunov Exponents 33 §2.1. Lyapunov exponents and their basic properties 33 §2.2. The Lyapunov and Perron regularity coefficients 38 §2.3. Lyapunov exponents for linear differential equations 41 §2.4. Forward and backward regularity. The Lyapunov-Perron regularity 51 §2.5. Lyapunov exponents for sequences of matrices 56 Chapter 3. Lyapunov Stability Theory of Nonautonomous Equations 61 §3.1. Stability of solutions of ordinary differential equations 62 §3.2. Lyapunov absolute stability theorem 68 §3.3. Lyapunov conditional stability theorem 72
IV Contents Chapter 4. Elements of the Nonuniform Hyperbolicity Theory 77 §4.1. Dynamical systems with nonzero Lyapunov exponents 78 §4.2. Nonuniform complete hyperbolicity 88 §4.3. Regular sets 91 §4.4. Nonuniform partial hyperbolicity 93 §4.5. Holder continuity of invariant distributions 94 Chapter 5. Cocycles over Dynamical Systems 99 §5.1. Cocycles and linear extensions 100 §5.2. Lyapunov exponents and Lyapunov-Perron regularity for cocycles 105 §5.3. Examples of measurable cocycles over dynamical systems 109 Chapter 6. The Multiplicative Ergodic Theorem 113 §6.1. Lyapunov-Perron regularity for sequences of triangular matrices 114 §6.2. Proof of the Multiplicative Ergodic Theorem 120 §6.3. Normal forms of measurable cocycles 124 §6.4. Lyapunov charts 128 Chapter 7. Local Manifold Theory 133 §7.1. Local stable manifolds 134 §7.2. An abstract version of the Stable Manifold Theorem 137 §7.3. Basic properties of stable and unstable manifolds 147 Chapter 8. Absolute Continuity of Local Manifolds 155 §8.1. Absolute continuity of the holonomy map 157 §8.2. A proof of the absolute continuity theorem 161 §8.3. Computing the Jacobian of the holonomy map 167 §8.4. An invariant foliation that is not absolutely continuous 168 Chapter 9. Ergodic Properties of Smooth Hyperbolic Measures 171 §9.1. Ergodicity of smooth hyperbolic measures 171 §9.2. Local ergodicity 176 §9.3. The entropy formula 183
Contents v Chapter 10. Geodesic Flows on Surfaces of Nonpositive Curvature 195 §10.1. Preliminary information from Riemannian geometry 196 §10.2. Definition and local properties of geodesic flows 198 §10.3. Hyperbolic properties and Lyapunov exponents 200 §10.4. Ergodic properties 205 §10.5. The entropy formula for geodesic flows 210 Part 2. Selected Advanced Topics Chapter 11. Cone Technics 215 §11.1. Introduction 215 §11.2. Lyapunov functions 217 §11.3. Cocycles with values in the symplectic group 221 Chapter 12. Partially Hyperbolic Diffeomorphisms with Nonzero Exponents 223 §12.1. Partial hyperbolicity 224 §12.2. Systems with negative central exponents 227 §12.3. Foliations that are not absolutely continuous 229 Chapter 13. More Examples of Dynamical Systems with Nonzero Lyapunov Exponents 235 §13.1. Hyperbolic diffeomorphisms with countably many ergodic components 235 §13.2. The Shub-Wilkinson map 246 Chapter 14. Anosov Rigidity 247 §14.1. The Anosov rigidity phenomenon. I 247 §14.2. The Anosov rigidity phenomenon. II 255 Chapter 15. C 1 Pathological Behavior: Pugh’s Example 261 Bibliography 267 Index 273
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:43:39Z |
| institution | BVB |
| isbn | 9780821898536 |
| language | English |
| lccn | 2013007773 |
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| physical | IX, 277 S. 26 cm |
| publishDate | 2013 |
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| publisher | American Mathematical Soc. |
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| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Barreira, Luis 1968- Verfasser (DE-588)128529717 aut Introduction to smooth ergodic theory Luis Barreira ; Yakov Pesin Providence, RI American Mathematical Soc. 2013 IX, 277 S. 26 cm txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 148 Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s DE-604 Pesin, Yakov B. 1946- Verfasser (DE-588)129370533 aut Erscheint auch als Online-Ausgabe 978-1-4704-0972-2 Graduate studies in mathematics 148 (DE-604)BV009739289 148 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026244054&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barreira, Luis 1968- Pesin, Yakov B. 1946- Introduction to smooth ergodic theory Graduate studies in mathematics Ergodentheorie (DE-588)4015246-7 gnd |
| subject_GND | (DE-588)4015246-7 |
| title | Introduction to smooth ergodic theory |
| title_auth | Introduction to smooth ergodic theory |
| title_exact_search | Introduction to smooth ergodic theory |
| title_full | Introduction to smooth ergodic theory Luis Barreira ; Yakov Pesin |
| title_fullStr | Introduction to smooth ergodic theory Luis Barreira ; Yakov Pesin |
| title_full_unstemmed | Introduction to smooth ergodic theory Luis Barreira ; Yakov Pesin |
| title_short | Introduction to smooth ergodic theory |
| title_sort | introduction to smooth ergodic theory |
| topic | Ergodentheorie (DE-588)4015246-7 gnd |
| topic_facet | Ergodentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026244054&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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