03765nam 2200589 450 991048087310332120180731044357.01-4704-0401-X(CKB)3360000000464987(EBL)3114087(SSID)ssj0000973476(PQKBManifestationID)11552373(PQKBTitleCode)TC0000973476(PQKBWorkID)10959982(PQKB)10522863(MiAaPQ)EBC3114087(PPN)195416902(EXLCZ)99336000000046498720150417h20042004 uy 0engur|n|---|||||txtccrErgodic theory of equivariant diffeomorphisms Markov partitions and stable ergodicity /Michael Field, Matthew NicolProvidence, Rhode Island :American Mathematical Society,2004.©20041 online resource (113 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 169, Number 803"Volume 169, Number 803 (end of volume)."0-8218-3599-8 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;Volume 169, Number 803.Ergodic theoryDiffeomorphismsElectronic books.Ergodic theory.Diffeomorphisms.515.48Field Mike56769Nicol MatthewMiAaPQMiAaPQMiAaPQBOOK9910480873103321Ergodic theory of equivariant diffeomorphisms2036000UNINA