Mathematical problems of statistical mechanics and dynamics: a collection of surveys
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht ; Bosten ; Lancaster ; Tokyo
Reidel Publishing Company
[1986]
|
| Schriftenreihe: | Mathematics and its applications / Soviet series
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiv, 261 Seiten Illustrationen |
| ISBN: | 9027721831 9789401085403 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematical problems of statistical mechanics and dynamics |b a collection of surveys |c R. L. Dobrushin, Institute of Information Transmission Problems, Academy of Sciences, Moscow, U.S.S.R. |
| 264 | 1 | |a Dordrecht ; Bosten ; Lancaster ; Tokyo |b Reidel Publishing Company |c [1986] | |
| 264 | 4 | |c © 1986 | |
| 300 | |a xiv, 261 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications / Soviet series |v 6 | |
| 650 | 7 | |a Dynamique |2 ram | |
| 650 | 7 | |a Mécanique statistique - Modèles mathématiques |2 ram | |
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| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
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| 810 | 2 | |a Soviet series |t Mathematics and its applications |v 6 |w (DE-604)BV004708148 |9 6 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000408004&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |n oe | |
Datensatz im Suchindex
| _version_ | 1805074172496314368 |
|---|---|
| adam_text |
Contents
Editor's Preface ix
Introduction xi
R. L. DOBRUSHIN AND M. ZAHRADNIK/Phase Diagrams for
Continuous Spin Models: An Extension of the Pirogov Sinai Theory 1
Introduction 1
1. Formulation of the Main Result 4
1.1. Configurations 4
1.2. States 4
1.3. Hamiltonians 5
1.4. Gibbs States 5
1.5. Assumptions of the Main Theorem 6
1.6. The Main Theorem 10
1.7. Strategy of the Proof 11
2. Preliminaries 11
2.1. Abstract Polymer Models and Cluster Expansions 11
2.2. Gaussian Gibbsian Fields: The Correlation Decay 17
2.3. Estimates of Semi Invariants: Cluster Expansions of Perturbed
Gaussian Fields 30
3. The Main Lemma 62
3.1. The Geometry of Configurations 62
3.2. Reduction to the Main Lemma 64
4. Proof of the Main Lemma 76
4.1. Contours 76
4.2. Reduction to a Contour Model 79
4.3. Estimates of the Main Term G JX). Decomposition of the
Contour Energy 88
4.4. Boundary Terms of Partition Functions of Contour Models 95
4.5. Conclusion of the Proof of the Main Lemma 106
References 122
N. I. CHERNOV/Space Time Entropy of Infinite Classical Systems 125
1. Introduction 125
2. Statistical Estimates of the Gibbs Distribution 126
3. Reduction to Partial Flows 129
4. Estimate of Space Time Entropy 132
References 136
vi CONTENTS
R. A. MINLOS AND A. I. MOGILNER / Spectrum Analysis and
Scattering Theory for a Three Particle Cluster Operator 139
1. Introduction. A General Definition of the Cluster Operator 139
2. Three Particle Cluster Operators 140
3. Equations for the Resolvent of a Self Adjoint Three Particle Cluster
Operator 143
4. Study of Equations (3.4) (3.6) 146
5. The Main Result 155
6. Proof of Theorem 5.11 (Scattering Theory) 157
References 160
M. L. BLANK/Stochastic Attractors and their Small Perturbations 161
1. Introduction 161
2. Dynamical Systems with Stochastic Attractors 164
3. Stochastic Perturbations (Regular Case) 170
4. The Law of Exponential Decay and Small Stochastic Perturbations 176
5. Stochastic Perturbations (Singular Case) 17.9
6. Small Quasi Stochastic Perturbations 180
7. Ergodic Properties of Dynamical System Discretizations 184
References 196
N. N. CENCOVA/Statistical Properties of Smooth Smale Horseshoes 199
Introduction 199
1. General Background 203
1.1. Structures in the Product I = X x Y 203
1.2. Uniformly Hyperbolic Transformations of Z = X x Y 204
1.3. A Sufficient Condition for Uniform Hyperbolicity in I = X x Y 206
1.4. Leaves and Rectangles 207
1.5. The Smale Horseshoe 209
2. Expanding and Contracting Fibrations of a Smale Horseshoe 211
2.1. The Smoothness of Expanding and Contracting Fibres 211
2.2. Expanding and Contracting Fibrations are Holderian 213
2.3. The Local Smoothness of Expanding and Contracting Fibrations 213
2.4. The Holder Property of the Canonical Isomorphism Defined
byaFibration 215
3. Smooth Invariant Conditional Probability Distributions on Fibrations 216
3.1. The Evolution of Densities of Conditional Probability
Distributions on Fibres Induced by 3~ 216
3.2. The Existence of a T Invariant Smooth Family of Probability
Distributions on Fibres at 0(oo) 217
3.3. Comparison of Densities of Conditional Probability Distributions
on Different Fibres 218
3.4. The Dependence of T Invariant Conditional Densities on the
Number of the Fibre 219
4. Smooth Non Singular Probability Distributions on a Smale
Horseshoe 220
CONTENTS. vii
4.1. Defining Measures on Measurable Rectangles in Terms of
Conditional Probability Distributions on Fibres 220
4.2. An Average Description of the Evolution of Measures from the
Class S 222
4.3. The Construction of an Eigenmeasure for a Smale Horseshoe 224
5. A Natural Invariant Probability Distribution on the Hyperbolic Set
of a Smale Horseshoe 226
5.1. The Sequence of Probability Distributions fi(m) 226
5.2. The Computation of the Asymptotics of fi(m) via the Matrix
Technique 228
5.3. The Weak Limit//0{"} of the Sequence of Measures/i(m){ } 233
6. Some Properties of the Constructed Limit Probability Distributions
on a Smale Horseshoe 235
6.1. The ^Invariant Conditional Probability Distributions P{ \1) on
Expanding Fibres of the Hyperbolic Set Q 235
6.2. Weak Bernoulli Partition for the T Invariant Measure /*0 236
6.3. The Eigenfunction e(I) of a Smale Horseshoe 239
7. Evolution of Probability Distributions on a Smale Horseshoe 240
7.1. Asymptotic Inequalities for Measures and Integrals 240
7.2. The Asymptotics of Integrals 244
7.3. Mappings Which Possess a Smale Horseshoe 250
Appendix: Ergodic Properties of Positive Matrices with Bounded Ratio
of Rows 253
References 256
Author Index 257
Subject Index 259 |
| any_adam_object | 1 |
| author2 | Dobrušin, R. L. 1929-1995 |
| author2_role | edt |
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| author_GND | (DE-588)174089635 |
| author_facet | Dobrušin, R. L. 1929-1995 |
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| dewey-full | 530.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13 |
| dewey-search | 530.13 |
| dewey-sort | 3530.13 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-20T05:21:17Z |
| institution | BVB |
| isbn | 9027721831 9789401085403 |
| language | English |
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| physical | xiv, 261 Seiten Illustrationen |
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| spelling | Mathematical problems of statistical mechanics and dynamics a collection of surveys R. L. Dobrushin, Institute of Information Transmission Problems, Academy of Sciences, Moscow, U.S.S.R. Dordrecht ; Bosten ; Lancaster ; Tokyo Reidel Publishing Company [1986] © 1986 xiv, 261 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 6 Dynamique ram Mécanique statistique - Modèles mathématiques ram Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Statistische Mechanik (DE-588)4056999-8 s Mathematik (DE-588)4037944-9 s DE-604 Dynamisches System (DE-588)4013396-5 s Stochastischer Prozess (DE-588)4057630-9 s Dobrušin, R. L. 1929-1995 (DE-588)174089635 edt Erscheint auch als Online-Ausgabe 978-94-009-4592-0 Soviet series Mathematics and its applications 6 (DE-604)BV004708148 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000408004&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathematical problems of statistical mechanics and dynamics a collection of surveys Dynamique ram Mécanique statistique - Modèles mathématiques ram Statistische Mechanik (DE-588)4056999-8 gnd Dynamisches System (DE-588)4013396-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4056999-8 (DE-588)4013396-5 (DE-588)4057630-9 (DE-588)4037944-9 (DE-588)4143413-4 |
| title | Mathematical problems of statistical mechanics and dynamics a collection of surveys |
| title_auth | Mathematical problems of statistical mechanics and dynamics a collection of surveys |
| title_exact_search | Mathematical problems of statistical mechanics and dynamics a collection of surveys |
| title_full | Mathematical problems of statistical mechanics and dynamics a collection of surveys R. L. Dobrushin, Institute of Information Transmission Problems, Academy of Sciences, Moscow, U.S.S.R. |
| title_fullStr | Mathematical problems of statistical mechanics and dynamics a collection of surveys R. L. Dobrushin, Institute of Information Transmission Problems, Academy of Sciences, Moscow, U.S.S.R. |
| title_full_unstemmed | Mathematical problems of statistical mechanics and dynamics a collection of surveys R. L. Dobrushin, Institute of Information Transmission Problems, Academy of Sciences, Moscow, U.S.S.R. |
| title_short | Mathematical problems of statistical mechanics and dynamics |
| title_sort | mathematical problems of statistical mechanics and dynamics a collection of surveys |
| title_sub | a collection of surveys |
| topic | Dynamique ram Mécanique statistique - Modèles mathématiques ram Statistische Mechanik (DE-588)4056999-8 gnd Dynamisches System (DE-588)4013396-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Dynamique Mécanique statistique - Modèles mathématiques Statistische Mechanik Dynamisches System Stochastischer Prozess Mathematik Aufsatzsammlung |
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