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Dynamical systems: 9 Dynamical systems with hyperbolic behavior

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Bibliographic Details
Other Authors:	Anosov, Dmitrij V. 1936-2014 (Editor)
Format:	Book
Language:	English
Published:	Berlin <<[u.a.]>> Springer 1995
Series:	Encyclopaedia of mathematical sciences 66
Online Access:	Inhaltsverzeichnis
Physical Description:	235 S. graph. Darst.
ISBN:	3540570438 0387570438

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MARC


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adam_text	D.VANOSOV (ED.) DYNAMICAL SYSTEMS IX DYNAMICAL SYSTEMS WITH HYPERBOLIC BEHAVIOUR WITH 39 FIGURES SPRINGER DYNAMICAL SYSTEMS WITH HYPERBOLIC BEHAVIOUR D.V. ANOSOV, S.KH. ARANSON, V.Z. GRINES, R.V. PLYKIN, A.V. SAFONOV, E.A. SATAEV, S.V. SHLYACHKOV, V.V. SOLODOV, A.N. STARKOV, A.M. STEPIN TRANSLATED FROM THE RUSSIAN BY G.G. GOULD CONTENTS PREFACE {D. V. ANOSOV) 4 REFERENCES 9 CHAPTER 1. HYPERBOLIC SETS (D. V. ANOSOV, V. V. SOLODOV) 10 §1. PRELIMINARY NOTIONS 10 1.1. DEFINITION OF A HYPERBOLIC SET 10 1.2. COMMENTS 16 1.3. STABLE AND UNSTABLE MANIFOLDS 21 1.4. STABLE AND UNSTABLE MANIFOLDS IN CERTAIN SPECIAL CASES .... 27 §2. SOME EXAMPLES 31 2.1. HETEROCLINIC AND HOMOCLINIC POINTS 31 2.2. THE SMALE HORSESHOE 34 2.3. MOTIONS IN A NEIGHBOURHOOD OF A HOMOCLINIC TRAJECTORY. E-TRAJECTORIES 46 2.4. MARKOV PARTITIONING FOR A HYPERBOLIC AUTOMORPHISM OF A TWO-DIMENSIONAL TORUS 51 2 CONTENTS §3. SEMILOCAL THEORY 54 3.1. E-TRAJECTORIES 54 3.2. LOCALLY MAXIMAL HYPERBOLIC SETS 59 3.3. REMARKS 64 §4. GLOBAL THEORY 70 4.1. SMALE S AXIOM A AND STRUCTURAL STABILITY 70 4.2. ANOSOV SYSTEMS 74 4.3. REMARKS 78 4.4. BEYOND THE LIMITS OF HYPERBOLICITY 81 REFERENCES 84 CHAPTER 2. STRANGE ATTRACTORS (R. V. PLYKIN, E.A. SATAEV, S. V. SHLYACHKOV) 93 INTRODUCTION 93 §1. HYPERBOLIC ATTRACTORS 94 1.1. QUASI-ATTRACTORS RELATED TO THE HORSESHOE 94 1.2. ATTRACTORS OF CODIMENSION 1 95 1.3. ONE-DIMENSIONAL ATTRACTORS 99 §2. THE LORENZ ATTRACTOR 103 2.1. PHYSICAL MODELS LEADING TO A LORENZ SYSTEM 103 2.2. BIFURCATION IN A LORENZ SYSTEM 105 2.3. FIRST-RETURN MAP 106 2.4. INVARIANT STABLE FOLIATION 112 2.5. INVARIANT UNSTABLE FOLIATION 114 2.6. LACUNAE 115 2.7. CLASSIFICATION THEOREM 118 2.8. STRUCTURALLY STABLE AND STRUCTURALLY UNSTABLE PROPERTIES ... 119 2.9. A CONTINUUM OF NON-HOMEOMORPHIC ATTRACTORS 121 2.10. AN ALTERNATIVE TREATMENT OF THE ATTRACTOR IN A LORENZ SYSTEM 122 §3. METRIC PROPERTIES OF ONE-DIMENSIONAL ATTRACTORS OF HYPERBOLIC MAPS WITH SINGULARITIES 125 3.1. OBJECTS OF INVESTIGATION 125 3.2. INVARIANT U-GIBBS MEASURES 127 APPLICATION. E-TRAJECTORIES AND STABILITY PROPERTIES OF DYNAMICAL SYSTEMS 129 REFERENCES 135 CHAPTER 3. CASCADES ON SURFACES (S.KH. ARANSON, V.Z. GRINES) 141 §1. MORSE-SMALE DIFFEOMORPHISMS 141 §2. CASCADES WITH A COUNTABLE SET OF PERIODIC POINTS 146 2.1. TOPOLOGICAL CLASSIFICATION OF BASIC SETS 146 CONTENTS 3 2.2. TOPOLOGICAL CLASSIFICATION OF *-DIFFEOMORPHISMS WITH NON-TRIVIAL BASIC SETS AND HOMEOMORPHISMS WITH TWO INVARIANT TRANSVERSAL FOLIATIONS 149 §3. VARIOUS APPROACHES TO THE PROBLEM OF THE REALIZATION OF HOMOTOPY CLASSES OF HOMEOMORPHISMS WITH GIVEN TOPOLOGICAL PROPERTIES 157 3.1. GEODESIC LAMINATIONS AND THEIR ROLE IN THE CONSTRUCTION OF REPRESENTATIVES OF HOMOTOPY CLASSES OF HOMEOMORPHISMS .. 157 3.2. THE NIELSEN-THURSTON THEORY ON THE HOMOTOPY CLASSIFICATION OF HOMEOMORPHISMS OF SURFACES 164 REFERENCES 171 CHAPTER 4. DYNAMICAL SYSTEMS WITH TRANSITIVE SYMMETRY GROUP. GEOMETRIC AND STATISTICAL PROPERTIES (A. V. SAFONOV, A.N. STARKOV, A.M. STEPIRI) 177 INTRODUCTION 177 §1. BASIC CONCEPTS AND CONSTRUCTIONS. EXAMPLES 179 §2. A CRITERION FOR ERGODICITY AND THE ERGODIC DECOMPOSITION 185 §3. SPECTRUM OF ERGODIC FLOWS ON HOMOGENEOUS SPACES 192 §4. ORBITS OF HOMOGENEOUS FLOWS 199 §5. STATISTICAL PROPERTIES OF G-INDUCED FLOWS (AND ACTIONS) 207 §6. RIGIDITY OF HOMOGENEOUS FLOWS 213 APPENDIX A. STRUCTURE OF SPACES OF FINITE VOLUME 217 APPENDIX B. CONSTRUCTION OF SEMISIMPLE SPLITTING OF SIMPLY CONNECTED LIE GROUPS 222 ADDED TO THE ENGLISH TRANSLATION 224 REFERENCES 225 AUTHOR INDEX 231 SUBJECT INDEX 233 »
any_adam_object	1
author2	Anosov, Dmitrij V. 1936-2014
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author_GND	(DE-588)131836153
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dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	515 - Analysis
dewey-raw	515.352
dewey-search	515.352
dewey-sort	3515.352
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
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physical	235 S. graph. Darst.
publishDate	1995
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spelling	Dinamičeskie sistemy Dynamical systems 9 Dynamical systems with hyperbolic behavior D. V. Anosov (ed.). [Authors D. V. Anosov ... Transl. G. G. Gould] Berlin <<[u.a.]>> Springer 1995 235 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopaedia of mathematical sciences 66 Encyclopaedia of mathematical sciences ... Anosov, Dmitrij V. 1936-2014 (DE-588)131836153 edt (DE-604)BV023545761 9 Encyclopaedia of mathematical sciences 66 (DE-604)BV024126459 66 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017207743&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Dynamical systems Encyclopaedia of mathematical sciences
title	Dynamical systems
title_alt	Dinamičeskie sistemy
title_auth	Dynamical systems
title_exact_search	Dynamical systems
title_full	Dynamical systems 9 Dynamical systems with hyperbolic behavior D. V. Anosov (ed.). [Authors D. V. Anosov ... Transl. G. G. Gould]
title_fullStr	Dynamical systems 9 Dynamical systems with hyperbolic behavior D. V. Anosov (ed.). [Authors D. V. Anosov ... Transl. G. G. Gould]
title_full_unstemmed	Dynamical systems 9 Dynamical systems with hyperbolic behavior D. V. Anosov (ed.). [Authors D. V. Anosov ... Transl. G. G. Gould]
title_short	Dynamical systems
title_sort	dynamical systems dynamical systems with hyperbolic behavior
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017207743&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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