Positive transfer operators and decay of correlations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2000
|
| Series: | Advanced series in nonlinear dynamics
16 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | X, 314 S. |
| ISBN: | 9810233280 |
Staff View
MARC
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| 245 | 1 | 0 | |a Positive transfer operators and decay of correlations |c Viviane Baladi |
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| 490 | 1 | |a Advanced series in nonlinear dynamics |v 16 | |
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Record in the Search Index
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| adam_text | Contents
Preface v
Chapter 1 Subshifts of finite type: A key symbolic model 1
1.1 Introduction 1
1.2 Finite range interactions (Perron Frobenius) 2
1.3 Exponentially decaying interactions 28
1.4 Non Holder interactions 59
1.5 Historical and bibliographical notes 67
Chapter 2 Smooth uniformly expanding dynamics 71
2.1 Introduction 71
2.2 Smooth invariant measures 74
2.3 One dimensional differentiable case (spectrum) 86
2.4 Higher dimensions 92
2.5 The analytic case: Nuclearity 96
2.5.1 Nuclear operators, traces, and determinants 97
2.5.2 Three analytic applications 106
2.6 Dynamical zeta functions and determinants 112
2.7 Stochastic spectral stability 119
2.7.1 SRB case 121
2.7.2 Non SRB case and zeta functions 135
2.8 Historical and bibliographical notes 139
Chapter 3 Piecewise expanding systems 145
3.1 Introduction 145
ix
X Contents
3.2 Uniform expansion 148
3.3 Stochastic stability of spectrum 169
3.4 Nonuniform expansion: Exponential mixing 184
3.5 Nonuniform expansion: Nonexponential mixing 210
3.6 Historical and bibliographical notes 219
Chapter 4 Hyperbolic systems 225
4.1 Introduction 225
4.1.1 Linear hyperbolic toral automorphisms 225
4.1.2 Physical measures and SRB measures 228
4.1.3 Strategies for constructing SRB measures 239
4.2 Reducing to expanding: Finite Markov partitions 242
4.3 Reducing to expanding: Countable Markov towers 247
4.4 Hyperbolic transfer operators 269
4.4.1 Hyperbolic analytic surface diffeomorphisms 269
4.4.2 Cones for smooth hyperbolic diffeomorphisms 288
4.5 Historical and bibliographical notes 291
Bibliography 293
Index 311
Contents Preface v Chapter 1 Subshifts of finite type: A key symbolic model 1.1 Introduction....................................................................................... 1.2 Finite range interactions (Perron-Frobenius) ............................ 1.3 Exponentially decaying interactions ........................................... 1.4 Non-Hölder interactions................................................................. 1.5 Historical and bibliographical notes.............................................. Chapter 2 Smooth uniformly expanding dynamics 2.1 Introduction...................................................................................... 2.2 Smooth invariant measures........................................................... 2.3 One-dimensional differentiable case (spectrum)......................... 2.4 Higher dimensions.......................................................................... 2.5 The analytic case: Nuclearity....................................................... 2.5.1 Nuclear operators, traces, and determinants...................... 2.5.2 Three analytic applications............................................... 2.6 Dynamical zeta functions and determinants............................... 2.7 Stochastic spectral stability........................................................... 2.7.1 SRB case.............................................................................. 2.7.2 Non-SRB case and zeta functions ...................................... 2.8 Historical and bibliographical
notes............................................... 1 1 2 28 59 67 71 71 74 86 92 96 97 106 112 119 121 135 139 Chapter 3 Piecewise expanding systems 145 3.1 Introduction....................................................................................... 145 ix
Contents x 3.2 3.3 3.4 3.5 3.6 Uniform expansion........................................................................... Stochastic stability of spectrum..................................................... Nonuniform expansion: Exponential mixing................................ Nonuniform expansion: Nonexponential mixing......................... Historical and bibliographical notes............................................... 148 169 184 210 219 Chapter 4 Hyperbolic systems 225 4.1 Introduction....................................................................................... 225 4.1.1 Linear hyperbolic toral automorphisms ......................... 225 4.1.2 Physical measures and SRB measures................................ 228 4.1.3 Strategies for constructing SRB measures..................... 239 4.2 Reducing to expanding: Finite Markov partitions...................... 242 4.3 Reducing to expanding: Countable Markov towers................... 247 4.4 Hyperbolic transfer operators......................................................... 269 4.4.1 Hyperbolic analytic surface diffeomorphisms................... 269 4.4.2 Cones for smooth hyperbolic diffeomorphisms ................ 288 4.5 Historical and bibliographical notes............................................... 291 Bibliography 293 Index 311
|
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| dewey-ones | 510 - Mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV013483873 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:46:39Z |
| institution | BVB |
| isbn | 9810233280 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009203154 |
| oclc_num | 45230894 |
| open_access_boolean | |
| owner | DE-29T DE-384 DE-188 DE-739 |
| owner_facet | DE-29T DE-384 DE-188 DE-739 |
| physical | X, 314 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | World Scientific |
| record_format | marc |
| series | Advanced series in nonlinear dynamics |
| series2 | Advanced series in nonlinear dynamics |
| spelling | Baladi, Viviane 1963- Verfasser (DE-588)1089188501 aut Positive transfer operators and decay of correlations Viviane Baladi Singapore [u.a.] World Scientific 2000 X, 314 S. txt rdacontent n rdamedia nc rdacarrier Advanced series in nonlinear dynamics 16 Chaos gtt Correlatieanalyse gtt Niet-lineaire dynamica gtt Operadores lineares larpcal Operadores larpcal Positieve operatoren gtt Linear operators Transferoperator (DE-588)4846596-3 gnd rswk-swf Ergodensatz (DE-588)4152756-2 gnd rswk-swf Zeitdiskretes System (DE-588)4127297-3 gnd rswk-swf Transferoperator (DE-588)4846596-3 s Zeitdiskretes System (DE-588)4127297-3 s Ergodensatz (DE-588)4152756-2 s DE-604 Advanced series in nonlinear dynamics 16 (DE-604)BV004464593 16 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009203154&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009203154&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baladi, Viviane 1963- Positive transfer operators and decay of correlations Advanced series in nonlinear dynamics Chaos gtt Correlatieanalyse gtt Niet-lineaire dynamica gtt Operadores lineares larpcal Operadores larpcal Positieve operatoren gtt Linear operators Transferoperator (DE-588)4846596-3 gnd Ergodensatz (DE-588)4152756-2 gnd Zeitdiskretes System (DE-588)4127297-3 gnd |
| subject_GND | (DE-588)4846596-3 (DE-588)4152756-2 (DE-588)4127297-3 |
| title | Positive transfer operators and decay of correlations |
| title_auth | Positive transfer operators and decay of correlations |
| title_exact_search | Positive transfer operators and decay of correlations |
| title_full | Positive transfer operators and decay of correlations Viviane Baladi |
| title_fullStr | Positive transfer operators and decay of correlations Viviane Baladi |
| title_full_unstemmed | Positive transfer operators and decay of correlations Viviane Baladi |
| title_short | Positive transfer operators and decay of correlations |
| title_sort | positive transfer operators and decay of correlations |
| topic | Chaos gtt Correlatieanalyse gtt Niet-lineaire dynamica gtt Operadores lineares larpcal Operadores larpcal Positieve operatoren gtt Linear operators Transferoperator (DE-588)4846596-3 gnd Ergodensatz (DE-588)4152756-2 gnd Zeitdiskretes System (DE-588)4127297-3 gnd |
| topic_facet | Chaos Correlatieanalyse Niet-lineaire dynamica Operadores lineares Operadores Positieve operatoren Linear operators Transferoperator Ergodensatz Zeitdiskretes System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009203154&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009203154&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004464593 |
| work_keys_str_mv | AT baladiviviane positivetransferoperatorsanddecayofcorrelations |
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