Basic ergodic theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Basel [u.a.]
Birkhäuser
1998
|
| Edition: | 2. ed. |
| Series: | Birkhäuser advanced texts
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 149 S. graph. Darst. |
| ISBN: | 3764358165 0817658165 |
Staff View
MARC
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| 245 | 1 | 0 | |a Basic ergodic theory |c M. G. Nadkarni |
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Record in the Search Index
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| adam_text | Contents
Preface to the First Edition vii
Preface to the Second Edition ix
1 The Poincare Recurrence Lemma
Standard Borel Spaces 2
Borel Automorphisms 3
Orbit Equivalence and Isomorphism 6
Poincare Recurrence Lemma 7
Asides 10
2 Ergodic Theorems of Birkhoff and von Neumann
Ergodic Theorem for Permutations 13
Easy Generalisations 15
Almost Periodic Functions 16
Birkhoff s Ergodic Theorem 20
von Neumann Ergodic Theorem 27
Ergodic Theorems for Return Times 29
Asides 31
3 Ergodicity
Discussion of Ergodicity 33
Irrational Rotation 36
Diadic Adding Machine 39
4 Mixing Conditions and Their Characterisations
5 Bernoulli Shift and Related Concepts
Bernoulli Shifts 51
Kolmogorov Consistency Theorem 54
Markov Shift 55
Kolmogorov Shifts and Related Concepts 56
Non Invertible Shifts 57
Diadic Adding Machine 57
Hewitt Savage Zero one Law 58
6 Discrete Spectrum Theorem
Spectral Isomorphism of Bernoulli Shifts 63
Entropy 63
vi Contents
7 Induced Automorphisms and Related Concepts
Kakutani Towers 65
Periodic Approximations 67
Rokhlin s Lemma 67
Induced Automorphisms 68
Automorphism Built Under a Function 69
Kakutani Equivalence 71
Rank of an Automorphism 72
Countable Generators 73
Rank of an Automorphism 75
8 Borel Automorphisms are Polish Homeomorphisms 79
9 The Glimm Eflros Theorem 83
10 E. Hopf s Theorem
Compressibility (in the Sense of Birkhoff and Smith) 93
Compressibility (in the Sense of Hopf) 95
Compressibility 96
Ergodic Theorem (Measure Free Proof) 99
Ergodic Decomposition 104
Proof of Hopf s Theorem 109
Orbit Equivalence 110
Generalisations and Counter Examples 111
11 H. Dye s Theorem 113
12 Flows and Their Representations
Definitions and Examples 125
Flow Built Under a Function 126
Topology for a Flow 128
Existence of Countable Cross Sections 131
Representation of Non singular Flows 134
Representation of Measure Preserving Flows 138
References 141
Index 147
|
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| author | Nadkarni, Mahendra G. 1939- |
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| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:22:25Z |
| institution | BVB |
| isbn | 3764358165 0817658165 |
| language | German |
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| physical | VI, 149 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Birkhäuser |
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| series2 | Birkhäuser advanced texts |
| spelling | Nadkarni, Mahendra G. 1939- Verfasser (DE-588)120671999 aut Basic ergodic theory M. G. Nadkarni 2. ed. Basel [u.a.] Birkhäuser 1998 VI, 149 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Birkhäuser advanced texts Théorie ergodique ram Ergodic theory Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008223348&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nadkarni, Mahendra G. 1939- Basic ergodic theory Théorie ergodique ram Ergodic theory Ergodentheorie (DE-588)4015246-7 gnd |
| subject_GND | (DE-588)4015246-7 |
| title | Basic ergodic theory |
| title_auth | Basic ergodic theory |
| title_exact_search | Basic ergodic theory |
| title_full | Basic ergodic theory M. G. Nadkarni |
| title_fullStr | Basic ergodic theory M. G. Nadkarni |
| title_full_unstemmed | Basic ergodic theory M. G. Nadkarni |
| title_short | Basic ergodic theory |
| title_sort | basic ergodic theory |
| topic | Théorie ergodique ram Ergodic theory Ergodentheorie (DE-588)4015246-7 gnd |
| topic_facet | Théorie ergodique Ergodic theory Ergodentheorie |
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