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

Format:

Book

Author/Creator:

Field, Mike, author.

Nicol, Matthew, author.

Series:

Memoirs of the American Mathematical Society ; Volume 169, Number 803.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 169, Number 803

Language:

English

Subjects (All):

Ergodic theory.

Diffeomorphisms.

Physical Description:

1 online resource (113 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2004.

Language Note:

English

Summary:

On the assumption that the $\Gamma$-orbits all have dimension equal to that of $\Gamma$, this title shows that there is a naturally defined $F$- and $\Gamma$-invariant measure $\nu$ of maximal entropy on $\Lambda$ (it is not assumed that the action of $\Gamma$ is free).

Contents:

""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""

Notes:

"Volume 169, Number 803 (end of volume)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0401-X