Equilibrium states in ergodic theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
[1998]
|
| Edition: | First published |
| Series: | London Mathematical Society: London Mathematical Society student texts
42 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | ix, 178 Seiten |
| ISBN: | 9780521595346 9781107359987 0521594200 0521595347 |
Staff View
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| 100 | 1 | |a Keller, Gerhard |d 1954- |0 (DE-588)131504177 |4 aut | |
| 245 | 1 | 0 | |a Equilibrium states in ergodic theory |c Gerhard Keller |
| 250 | |a First published | ||
| 264 | 1 | |a Cambridge |b Cambridge University Press |c [1998] | |
| 264 | 4 | |c © 1998 | |
| 300 | |a ix, 178 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society: London Mathematical Society student texts |v 42 | |
| 650 | 7 | |a Dynamique différentiabe |2 ram | |
| 650 | 7 | |a Ergodiciteit |2 gtt | |
| 650 | 7 | |a Evenwichten |2 gtt | |
| 650 | 7 | |a Théorie ergodique |2 ram | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Ergodic theory | |
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Record in the Search Index
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| adam_text |
Contents
Preface vii
1 Elementary examples of equilibrium states 1
1.1 Equilibrium states in finite systems 1
1.2 Systems on finite lattices 7
1.3 Invariant distributions for Markov matrices 12
1.4 Invariant measures for interval maps 13
2 Some basic ergodic theory 21
2.1 Birkhoff's ergodic theorem 21
2.2 Ergodicity and mixing 30
2.3 The ergodic decomposition 35
2.4 Return times and return maps 38
2.5 Factors and extensions 40
3 Entropy 43
3.1 Information and entropy of partitions 43
3.2 Entropy of dynamical systems 49
3.3 Entropy as a function of the measure 58
4 Equilibrium states and pressure 61
4.1 Pressure 61
4.2 Equilibrium states and the entropy function 66
4.3 Equilibrium states and convex geometry 73
4.4 The variational principle 78
4.5 Equilibrium states for expansive actions 89
5 Gibbs measures 95
5.1 Regular local energy functions 95
5.2 Gibbs measures are equilibrium states 99
5.3 Equilibrium states are Gibbs measures 103
5.4 Markov chains 108
5.5 Equilibrium states of the Ising model 109
vi CONTENTS
5.6 Large deviations for Gibbs measures 115
6 Equilibrium states and derivatives 123
6.1 Sinai Bowen Ruelle measures 124
6.2 Transfer operators 130
6.3 Absolutely continuous equilibrium states 135
6.4 Iterated function systems (IFS) 145
6.5 Pressure and dimension for IFS 147
A Appendix 157
A.I Lipschitz continuous functions 157
A.2 Some convex analysis in Rd 157
A.3 Non negative matrices 158
A.4 Some facts from probability and integration 159
A.5 Making discontinuous mappings continuous 166
References 169
List of special notations 174
Index 175 |
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| indexdate | 2024-09-06T00:22:04Z |
| institution | BVB |
| isbn | 9780521595346 9781107359987 0521594200 0521595347 |
| language | English |
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| physical | ix, 178 Seiten |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | London Mathematical Society: London Mathematical Society student texts |
| series2 | London Mathematical Society: London Mathematical Society student texts |
| spelling | Keller, Gerhard 1954- (DE-588)131504177 aut Equilibrium states in ergodic theory Gerhard Keller First published Cambridge Cambridge University Press [1998] © 1998 ix, 178 Seiten txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society student texts 42 Dynamique différentiabe ram Ergodiciteit gtt Evenwichten gtt Théorie ergodique ram Differentiable dynamical systems Ergodic theory Gleichgewicht (DE-588)4121372-5 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s Gleichgewicht (DE-588)4121372-5 s DE-604 Erscheint auch als Online-Ausgabe 978-1-107-35998-7 London Mathematical Society: London Mathematical Society student texts 42 (DE-604)BV000841726 42 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007935101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Keller, Gerhard 1954- Equilibrium states in ergodic theory London Mathematical Society: London Mathematical Society student texts Dynamique différentiabe ram Ergodiciteit gtt Evenwichten gtt Théorie ergodique ram Differentiable dynamical systems Ergodic theory Gleichgewicht (DE-588)4121372-5 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| subject_GND | (DE-588)4121372-5 (DE-588)4015246-7 |
| title | Equilibrium states in ergodic theory |
| title_auth | Equilibrium states in ergodic theory |
| title_exact_search | Equilibrium states in ergodic theory |
| title_full | Equilibrium states in ergodic theory Gerhard Keller |
| title_fullStr | Equilibrium states in ergodic theory Gerhard Keller |
| title_full_unstemmed | Equilibrium states in ergodic theory Gerhard Keller |
| title_short | Equilibrium states in ergodic theory |
| title_sort | equilibrium states in ergodic theory |
| topic | Dynamique différentiabe ram Ergodiciteit gtt Evenwichten gtt Théorie ergodique ram Differentiable dynamical systems Ergodic theory Gleichgewicht (DE-588)4121372-5 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| topic_facet | Dynamique différentiabe Ergodiciteit Evenwichten Théorie ergodique Differentiable dynamical systems Ergodic theory Gleichgewicht Ergodentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007935101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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