Ergodic theory of equivariant diffeomorphisms: Markov partitions and stable ergodicity
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2004
|
| Series: | Memoirs of the American Mathematical Society
803 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 169, number 803 (end of volume)." |
| Physical Description: | VIII, 100 S. graph. Darst. |
| ISBN: | 0821835998 |
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MARC
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| 245 | 1 | 0 | |a Ergodic theory of equivariant diffeomorphisms |b Markov partitions and stable ergodicity |c Michael Field ; Matthew Nicol |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2004 | |
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Introduction 1
Chapter 2. Equivariant Geometry and Dynamics 9
2.1. Lie groups, F manifolds and representations 9
2.1.1. Compact Lie groups 9
2.1.2. r manifolds 10
2.2. Equivariant dynamical systems 13
2.2.1. Discrete dynamical systems 13
2.2.2. Skew and principal extensions 14
2.2.3. Continuous dynamical systems 14
2.3. Local theory 14
2.4. Invariant subspaces and transversality 15
2.5. Basic sets for equivariant diffeomorphisms 10
Chapter 3. Technical preliminaries 19
3.1. Geometry of group actions and maps 19
3.1.1. Isotropy types and strata 19
3.1.2. Orbit stmcturc of twisted products 22
3.1.3. Equivariant vector fields 22
3.1.4. Equivariant maps of twisted products 23
3.2. Equivariant subshifts of finite type: F finite 24
3.2.1. Subshifts of finite type 24
3.3. Holder continuity and the Ruelle operator 25
3.4. Equilibrium states 27
Part 1. Markov partitions 29
Chapter 4. Markov partitions for finite group actions 31
4.1. Hyperbolicity 31
4.1.1. Local product structure 32
4.2. Markov partitions ; Equivariant symbolic dynamics 33
4.2.1. Symbolic dynamics for F basic sets 36
4.2.2. Markov partitions on A/F 38
4.3. Examples of symmetric hyperbolic basic sets: F finite 41
4.3.1. Equivariant horseshoes 41
V
vi CONTENTS
4.3.2. Equivariant attractors 42
4.4. Existence of F regular Markov partitions 43
Chapter 5. Transversally hyperbolic sets 47
5.1. Transverse hyperbolicity 47
5.1.1. Examples of transversally hyperbolic sets 49
5.2. Properties of transversally hyperbolic sets 50
5.3. F expansiveness 52
5.4. Stability properties of transversally hyperbolic sets 53
5.5. Subshifts of finite type and attr actors 54
5.6. Local product structure 55
5.7. Expansiveness and shadowing 56
5.8. Stability of basic sets 58
Chapter 6. Markov partitions for basic sets 59
6.1. Rectangles 59
6.2. Slices 60
6.3. Pre Markov partitions 60
6.4. Proper and admissible rectangles 62
6.5. F regular Markov partitions 64
6.6. Construction of F regular Markov partitions 67
Part 2. Stable Ergodicity 71
Chapter 7. Preliminaries 73
7.1. Metrics 73
7.2. The Haar lift 73
7.3. Isotropy and ergodicity 74
7.4. F regular Markov partitions 74
7.4.1. Holonomy transformations for basic sets 75
7.5. Measures on the orbit space 75
7.6. Spectral characterization of ergodicity and weak mixing 77
Chapter 8. Livsic regularity and ergodic components 79
8.1. Livsic regularity 79
8.2. Structure of ergodic components 81
Chapter 9. Stable Ergodicity 85
9.1. Stable ergodicity: F compact and connected 85
9.2. Stable ergodicity: F semisimple 88
9.3. Stable ergodicity for attractors 89
9.4. Stable ergodicity and SRB attractors 90
Appendix A. On the absolute continuity of v 93
CONTENTS vii
Appendix. Bibliography 97
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| indexdate | 2024-07-09T19:21:54Z |
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| isbn | 0821835998 |
| language | English |
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| physical | VIII, 100 S. graph. Darst. |
| publishDate | 2004 |
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| series2 | Memoirs of the American Mathematical Society |
| spelling | Field, Mike Verfasser aut Ergodic theory of equivariant diffeomorphisms Markov partitions and stable ergodicity Michael Field ; Matthew Nicol Providence, R.I. American Mathematical Society 2004 VIII, 100 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 803 "Volume 169, number 803 (end of volume)." Difeomorfismos larpcal Diffeomorfismen gtt Ergodiciteit gtt Teoria ergodica larpcal Diffeomorphisms Ergodic theory Diffeomorphismus (DE-588)4149767-3 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s Diffeomorphismus (DE-588)4149767-3 s DE-604 Nicol, Matthew Sonstige oth Memoirs of the American Mathematical Society 803 (DE-604)BV008000141 803 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010684190&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Field, Mike Ergodic theory of equivariant diffeomorphisms Markov partitions and stable ergodicity Memoirs of the American Mathematical Society Difeomorfismos larpcal Diffeomorfismen gtt Ergodiciteit gtt Teoria ergodica larpcal Diffeomorphisms Ergodic theory Diffeomorphismus (DE-588)4149767-3 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| subject_GND | (DE-588)4149767-3 (DE-588)4015246-7 |
| title | Ergodic theory of equivariant diffeomorphisms Markov partitions and stable ergodicity |
| title_auth | Ergodic theory of equivariant diffeomorphisms Markov partitions and stable ergodicity |
| title_exact_search | Ergodic theory of equivariant diffeomorphisms Markov partitions and stable ergodicity |
| title_full | Ergodic theory of equivariant diffeomorphisms Markov partitions and stable ergodicity Michael Field ; Matthew Nicol |
| title_fullStr | Ergodic theory of equivariant diffeomorphisms Markov partitions and stable ergodicity Michael Field ; Matthew Nicol |
| title_full_unstemmed | Ergodic theory of equivariant diffeomorphisms Markov partitions and stable ergodicity Michael Field ; Matthew Nicol |
| title_short | Ergodic theory of equivariant diffeomorphisms |
| title_sort | ergodic theory of equivariant diffeomorphisms markov partitions and stable ergodicity |
| title_sub | Markov partitions and stable ergodicity |
| topic | Difeomorfismos larpcal Diffeomorfismen gtt Ergodiciteit gtt Teoria ergodica larpcal Diffeomorphisms Ergodic theory Diffeomorphismus (DE-588)4149767-3 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| topic_facet | Difeomorfismos Diffeomorfismen Ergodiciteit Teoria ergodica Diffeomorphisms Ergodic theory Diffeomorphismus Ergodentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010684190&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT fieldmike ergodictheoryofequivariantdiffeomorphismsmarkovpartitionsandstableergodicity AT nicolmatthew ergodictheoryofequivariantdiffeomorphismsmarkovpartitionsandstableergodicity |