Thermodynamic formalism and holomorphic dynamical systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
Providence, RI
American Mathematical Society
2000
|
| Series: | Panoramas et synthèses
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 82 S. graph. Darst. |
| ISBN: | 0821819488 |
Staff View
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| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Ergodic theory | |
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| 650 | 4 | |a Thermodynamics | |
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Record in the Search Index
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| adam_text | Titel: Thermodynamic formalism and holomorphic dynamical systems
Autor: Zinsmeister, Michel
Jahr: 2000
Contents
Preface to the English Translation ix
Introduction 1
Chapter 1. The Ergodic Hypothesis 7
1.1. Statistical Mechanics of Continuous Systems 7
1.2. Measure Preserving Transformations 9
1.3. Ergodicity 10
1.4. Geometric Interpretation of Ergodicity 12
Chapter 2. The Concept of Entropy 15
2.1. A Little Classical Thermodynamics: Clausius Entropy 15
2.2. Entropy in Information Theory: Shannon s Entropy 17
2.3. Boltzmann s Entropy 21
Chapter 3. Entropy in Ergodic Theory 25
3.1. Physical Framework: Thermodynamics of Lattices 25
3.2. Entropy of an Invariant Measure 27
3.3. Topological Entropy and Pressure 30
3.4. Sub-shifts 32
Chapter 4. The Perron-Frobenius-Ruelle Theorem 35
4.1. Statement and Proof of the Theorem 35
4.2. Gibbs Measures and Equilibrium States 40
4.3. The Complex Ruelle Operator 44
Chapter 5. Conformal Repellers 47
5.1. Definition and General Properties 47
5.2. Examples 49
5.3. Calculation of the Hausdorff Dimension of J 52
Chapter 6. Iteration of Quadratic Polynomials 55
6.1. Fundamentals of Iteration 55
6.2. The Main Cardioid 57
6.3. Numerical Applications 60
6.4. Manning s Formula 61
6.5. Hausdorff Dimension of Jc for c in the Main Cardioid 64
6.6. The Hausdorff Dimension to Second Order Near 0 65
Chapter 7. Phase Transitions 69
7.1. Phase Transitions as Natural Phenomena 69
7.2. Theoretical Interpretation of Phase Transitions 71
CONTENTS
7.3. Parabolic Phase Transitions 72
Appendix A. Hausdorff Measures and Dimension 77
A.l. Standard Notions from Measure Theory 77
A.2. Hausdorff Measures 77
A.3. Hausdorff Dimension 78
Bibliography 81
|
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| dewey-tens | 510 - Mathematics |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:40:28Z |
| institution | BVB |
| isbn | 0821819488 |
| language | English French |
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| oclc_num | 42295988 |
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| physical | IX, 82 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Panoramas et synthèses |
| series2 | Société Mathématique de France: SMF AMS texts and monographs Panoramas et synthèses |
| spelling | Zinsmeister, Michel Verfasser aut Formalisme thermodynamique et systèmes dynamiques holomorphes Thermodynamic formalism and holomorphic dynamical systems Michel Zinsmeister Providence, RI American Mathematical Society 2000 IX, 82 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Société Mathématique de France: SMF AMS texts and monographs 2 Panoramas et synthèses 4 Dynamique différentiable Mesure, Théorie de la Sistemas dinâmicos holomorfos larpcal Teoria ergodica larpcal Thermodynamique Théorie ergodique Differentiable dynamical systems Ergodic theory Measure theory Thermodynamics Dynamisches System (DE-588)4013396-5 gnd rswk-swf Holomorphie (DE-588)4160484-2 gnd rswk-swf Thermodynamik (DE-588)4059827-5 gnd rswk-swf Holomorphie (DE-588)4160484-2 s Dynamisches System (DE-588)4013396-5 s Thermodynamik (DE-588)4059827-5 s DE-604 Société Mathématique de France SMF AMS texts and monographs 2 (DE-604)BV013184477 2 Panoramas et synthèses 4 (DE-604)BV037491878 4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008983634&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zinsmeister, Michel Thermodynamic formalism and holomorphic dynamical systems Panoramas et synthèses Dynamique différentiable Mesure, Théorie de la Sistemas dinâmicos holomorfos larpcal Teoria ergodica larpcal Thermodynamique Théorie ergodique Differentiable dynamical systems Ergodic theory Measure theory Thermodynamics Dynamisches System (DE-588)4013396-5 gnd Holomorphie (DE-588)4160484-2 gnd Thermodynamik (DE-588)4059827-5 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4160484-2 (DE-588)4059827-5 |
| title | Thermodynamic formalism and holomorphic dynamical systems |
| title_alt | Formalisme thermodynamique et systèmes dynamiques holomorphes |
| title_auth | Thermodynamic formalism and holomorphic dynamical systems |
| title_exact_search | Thermodynamic formalism and holomorphic dynamical systems |
| title_full | Thermodynamic formalism and holomorphic dynamical systems Michel Zinsmeister |
| title_fullStr | Thermodynamic formalism and holomorphic dynamical systems Michel Zinsmeister |
| title_full_unstemmed | Thermodynamic formalism and holomorphic dynamical systems Michel Zinsmeister |
| title_short | Thermodynamic formalism and holomorphic dynamical systems |
| title_sort | thermodynamic formalism and holomorphic dynamical systems |
| topic | Dynamique différentiable Mesure, Théorie de la Sistemas dinâmicos holomorfos larpcal Teoria ergodica larpcal Thermodynamique Théorie ergodique Differentiable dynamical systems Ergodic theory Measure theory Thermodynamics Dynamisches System (DE-588)4013396-5 gnd Holomorphie (DE-588)4160484-2 gnd Thermodynamik (DE-588)4059827-5 gnd |
| topic_facet | Dynamique différentiable Mesure, Théorie de la Sistemas dinâmicos holomorfos Teoria ergodica Thermodynamique Théorie ergodique Differentiable dynamical systems Ergodic theory Measure theory Thermodynamics Dynamisches System Holomorphie Thermodynamik |
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