Combinatorial constructions in ergodic theory and dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2003]
|
| Schriftenreihe: | University lecture series
Volume 30 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | iv, 121 Seiten |
| ISBN: | 0821834967 9780821834961 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804130211885744128 |
|---|---|
| adam_text | Table of Contents
0. Introduction 1
0.1. Theorems and constructions and ergodic theory 1
0.2. A little history 2
0.3. The story and purpose of these notes 3
0.4. Acknowledgements 4
Part I. Approximation and Genericity in Ergodic Theory 5
1. Periodic processes 5
2. Genericity of approximation 10
3. Various types of approximation 12
3.1. Cyclic approximation 12
3.2. Approximation of type (n, n + 1) 15
3.3. a weak mixing and singularity of convolutions 15
4. Spectral multiplicity of ergodic transformations 18
4.1. Essential value of spectral multiplicity 19
4.2. Transformations with arbitrary maximal spectral multiplicity 19
4.3. Cartesian powers and multiplicities bounded from below 22
4.4. Some recent results 26
5. Approximation and coding 27
6. Invariant measures for transformation with specification 37
7. Generic induced maps 42
8. Combinatorial approximation by conjugation construction 44
8.1. Introduction 44
8.2. General framework 45
8.3. Ergodicity and rotation factors 48
8.4. Non standard transformations 50
Part II. Cocycles, Cohomology and Combinatorial Constructions 53
9. Definitions and principal constructions 54
9.1. Cocycles, coboundaries and Mackey range 55
9.2. Lipschitz cocycles, pseudo isometries and the Ambrose Kakutani
theorem 58
iii
iv CONTENTS
9.3. Cohomological equations for measure preserving transformations
and flows 59
10. Structure of equivalence classes 62
10.1. Majorization and density in L1 62
10.2. Continuous and almost differentiable representations 66
11. Rigidity and stability 68
11.1. Definitions 68
11.2. Translations of the torus and smooth rigidity 70
11.3. Stability of Holder cocycles for transformations with specification 74
11.4. Livshitz theory 78
11.5. Invariant distributions and stability of partially hyperbolic systems 81
11.6. Stability determined by invariant distributions in parabolic systems 85
12. Wild cochains with tame coboundaries 89
12.1. Continuous cocycles over measure preserving homeomorphisms 90
12.2. Fast approximation and C°° cocycles 94
12.3. Minimal nonergodic diffeomorphisms of T2 97
12.4. Minimal nonergodic interval exchange transformations 98
13. Non trivial cocycles 102
13.1. Two general criteria 102
13.2. The case of fast C°° approximation 105
13.3. Weakly mixing flows on T2 107
13.4. Ergodicity of analytic cylindrical cascades 112
13.5. Weak mixing of special flows over interval exchange transforma¬
tions 114
References 117
|
| any_adam_object | 1 |
| author | Katok, Anatole 1944-2018 |
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| author_variant | a k ak |
| building | Verbundindex |
| bvnumber | BV017391840 |
| classification_rvk | SI 165 |
| ctrlnum | (OCoLC)441705374 (DE-599)BVBBV017391840 |
| dewey-full | 515.48 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.48 |
| dewey-search | 515.48 |
| dewey-sort | 3515.48 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017391840 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:17:26Z |
| institution | BVB |
| isbn | 0821834967 9780821834961 |
| language | English |
| lccn | 2003059582 |
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| physical | iv, 121 Seiten |
| publishDate | 2003 |
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| publisher | American Mathematical Society |
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| series | University lecture series |
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| spelling | Katok, Anatole 1944-2018 Verfasser (DE-588)111187125 aut Combinatorial constructions in ergodic theory and dynamics Anatole Katok Providence, Rhode Island American Mathematical Society [2003] © 2003 iv, 121 Seiten txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 30 Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s Differenzierbares dynamisches System (DE-588)4137931-7 s Kombinatorische Analysis (DE-588)4164746-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2175-5 University lecture series Volume 30 (DE-604)BV004153846 30 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010479347&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Katok, Anatole 1944-2018 Combinatorial constructions in ergodic theory and dynamics University lecture series Kombinatorische Analysis (DE-588)4164746-4 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| subject_GND | (DE-588)4164746-4 (DE-588)4137931-7 (DE-588)4015246-7 |
| title | Combinatorial constructions in ergodic theory and dynamics |
| title_auth | Combinatorial constructions in ergodic theory and dynamics |
| title_exact_search | Combinatorial constructions in ergodic theory and dynamics |
| title_full | Combinatorial constructions in ergodic theory and dynamics Anatole Katok |
| title_fullStr | Combinatorial constructions in ergodic theory and dynamics Anatole Katok |
| title_full_unstemmed | Combinatorial constructions in ergodic theory and dynamics Anatole Katok |
| title_short | Combinatorial constructions in ergodic theory and dynamics |
| title_sort | combinatorial constructions in ergodic theory and dynamics |
| topic | Kombinatorische Analysis (DE-588)4164746-4 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| topic_facet | Kombinatorische Analysis Differenzierbares dynamisches System Ergodentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010479347&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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