Ergodic theory of equivariant diffeomorphisms : Markov partitions and stable ergodicity / / Michael Field, Matthew Nicol

• Record Nr.: UNINA9910788746603321
• Autore: Field Mike
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2004; ©2004
• ISBN: 1-4704-0401-X
• Descrizione fisica: 1 online resource (113 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 169, Number 803
• Disciplina: 515.48
• Soggetti: Ergodic theory; Diffeomorphisms
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 169, Number 803 (end of volume)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Equivariant Geometry and Dynamics""; ""2.1. Lie groups, Î?-manifolds and representations""; ""2.1.1. Compact Lie groups""; ""2.1.2. Î?-manifolds""; ""2.2. Equivariant dynamical systems""; ""2.2.1. Discrete dynamical systems""; ""2.2.2. Skew and principal extensions""; ""2.2.3. Continuous dynamical systems""; ""2.3. Local theory""; ""2.4. Invariant subspaces and transversality""; ""2.5. Basic sets for equivariant diffeomorphisms""; ""Chapter 3. Technical preliminaries""; ""3.1. Geometry of group actions and maps""; ""4.4. Existence of Î?-regular Markov partitions""""Chapter 5. Transversally hyperbolic sets""; ""5.1. Transverse hyperbolicity""; ""5.2. Properties of transversally hyperbolic sets""; ""5.3. Î?-expansiveness""; ""5.4. Stability properties of transversally hyperbolic sets""; ""5.5. Subshifts of finite type and attractors""; ""5.6. Local product structure""; ""5.7. Expansiveness and shadowing""; ""5.8. Stability of basic sets""; ""Chapter 6. Markov partitions for basic sets""; ""6.1. Rectangles""; ""6.2. Slices""; ""6.3. Pre-Markov partitions""; ""6.4. Proper and admissible rectangles""; ""6.5. Î?-regular Markov partitions""""6.6. Construction of Î?-regular Markov partitions""; ""Part 2. Stable Ergodicity""; ""Chapter 7. Preliminaries""; ""7.1. Metrics""; ""7.2. The Haar lift""; ""7.3. Isotropy and ; ergodicity""; ""7.4. Î?-regular Markov partitions""; ""7.5. Measures on the orbit space""; ""7.6. Spectral characterization of ergodicity and weak-mixing""; ""Chapter 8. LivÅ¡ic regularity and ergodic components""; ""8.1. LivÅ¡ic regularity""; ""8.2. Structure of ergodic components""; ""Chapter 9. Stable Ergodicity""; ""9.1. Stable ergodicity: Î? compact and connected""; ""9.2. Stable ergodicity: Î? semisimple""""9.3. Stable ergodicity for attractors""; ""9.4. Stable ergodicity and SRB attractors""; ""Appendix A. On the absolute continuity of v""; ""Bibliography""