An introduction to infinite ergodic theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[1997]
|
| Series: | Mathematical surveys and monographs
Volume 50 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 284 Seiten |
| ISBN: | 0821804944 9780821804940 |
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MARC
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| 245 | 1 | 0 | |a An introduction to infinite ergodic theory |c Jon Aaronson |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1997] | |
| 264 | 4 | |c © 1997 | |
| 300 | |a xii, 284 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Mathematical surveys and monographs |v Volume 50 | |
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Record in the Search Index
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| adam_text | Contents
Contents be
Preface xi
Chapter 1. Non singular transformations 1
§1.0 Standard measure spaces 1
§1.1 Recurrence and conservativity 14
§1.2 Ergodicity 21
§1.3 The dual operator 33
§1.4 Invariant measures 36
§1.5 Induced transformations and applications 41
§1.6 Group actions and flows 48
Chapter 2. General ergodic and spectral theorems 53
§2.1 von Neumann s mean ergodic theorem 54
§2.2 Pointwise ergodic theorems 56
§2.3 Converses to Birkhoff s theorem 64
§2.4 Transformations with infinite invariant measures 70
§2.5 Spectral properties 73
§2.6 Eigenvalues 76
§2.7 Ergodicity of Cartesian products 81
Chapter 3. Transformations with infinite invariant measures 85
§3.1 Isomorphism, factors, and similarity 86
§3.2 Intrinsic normalising constants and laws of large numbers 93
§3.3 Rational ergodicity 98
§3.4 Maharam transformations 102
§3.5 Category theorems 108
§3.6 Asymptotic distributional behaviour 112
§3.7 Pointwise dual ergodicity 118
§3.8 Wandering rates 130
Chapter 4. Markov maps 139
§4.1 Markov partitions 139
§4.2 Graph shifts 140
§4.3 Distortion properties 143
§4.4 Ergodic properties of Markov maps with distortion properties 149
ix
x AN INTRODUCTION TO INFINITE ERGODIC THEORY
§4.5 Markov shifts 156
§4.6 Schweiger s jump transformation 161
§4.7 Smooth Probenius Perron operators and the Gibbs property 164
§4.8 Non expanding interval maps 172
§4.9 Additional reading 180
Chapter 5. Recurrent events and similarity of Markov shifts 181
§5.1 Renewal sequences 181
§5.2 Markov towers and recurrent events 183
§5.3 Kaluza sequences 188
§5.4 Similarity of Markov towers 191
§5.5 Random walks 194
Chapter 6. Inner functions 201
§6.1 Inner functions on the unit disc 201
§6.2 Inner functions on the upper half plane 208
§6.3 The dichotomy 212
§6.4 Examples 214
Chapter 7. Hyperbolic geodesic flows 223
§7.1 Hyperbolic space models 224
§7.2 The geodesic flow of H 227
§7.3 Asymptotic geodesies 229
§7.4 Surfaces 231
§7.5 The Poincare series 235
§7.6 Further results 246
Chapter 8. Cocycles and skew products 247
§8.1 Skew Products 247
§8.2 Persistencies and essential values 250
§8.3 Coboundaries 253
§8.4 Skew products over Kronecker transformations 256
§8.5 Joinings of skew products 264
§8.6 Squashable skew products over odometers 267
Bibliography 275
Index 281
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| indexdate | 2024-07-09T18:11:25Z |
| institution | BVB |
| isbn | 0821804944 9780821804940 |
| language | English |
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| physical | xii, 284 Seiten |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | American Mathematical Society |
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| series2 | Mathematical surveys and monographs |
| spelling | Aaronson, Jon 1949- Verfasser (DE-588)173112129 aut An introduction to infinite ergodic theory Jon Aaronson Providence, Rhode Island American Mathematical Society [1997] © 1997 xii, 284 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 50 Ergodentheorie Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1281-4 Mathematical surveys and monographs Volume 50 (DE-604)BV000018014 50 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007765269&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aaronson, Jon 1949- An introduction to infinite ergodic theory Mathematical surveys and monographs Ergodentheorie Ergodentheorie (DE-588)4015246-7 gnd |
| subject_GND | (DE-588)4015246-7 |
| title | An introduction to infinite ergodic theory |
| title_auth | An introduction to infinite ergodic theory |
| title_exact_search | An introduction to infinite ergodic theory |
| title_full | An introduction to infinite ergodic theory Jon Aaronson |
| title_fullStr | An introduction to infinite ergodic theory Jon Aaronson |
| title_full_unstemmed | An introduction to infinite ergodic theory Jon Aaronson |
| title_short | An introduction to infinite ergodic theory |
| title_sort | an introduction to infinite ergodic theory |
| topic | Ergodentheorie Ergodentheorie (DE-588)4015246-7 gnd |
| topic_facet | Ergodentheorie |
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