Geometric methods for discrete dynamical systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Oxford Univ. Press
1998
|
| Series: | The Oxford engineering science series
50 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 157 S. graph. Darst. |
| ISBN: | 0195085450 |
Staff View
MARC
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| 100 | 1 | |a Easton, Robert W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometric methods for discrete dynamical systems |c Robert W. Easton |
| 264 | 1 | |a New York [u.a.] |b Oxford Univ. Press |c 1998 | |
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Record in the Search Index
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| adam_text | Contents
1 Examples, 3
A. Logistic Maps, 4
B. Graphical Analysis, 5
C. Henon Maps, 9
D. The Standard Map Family, 12
E. Arnold s Circle Maps, 13
F. Quadratic Maps, 14
G. Duffing s Equation, 15
H. Interesting Maps, 16
I. Problems, 17
J. Further Reading, 17
2 Dynamical Systems, 18
A. Discrete and Continuous Dynamical Systems, 18
B. Omega Limit Sets, 21
C. Epsilon Chains, 25
D. The Conley Decomposition Theorem, 28
E. Directed Graphs, 30
F. Local Analysis of Orbits, 31
G. Summary, 33
H. Problems, 33
I. Further Reading, 34
3 Hyperbolic Fixed Points, 35
A. Linearization, 35
B. Stable and Unstable Manifolds, 39
C. Shadowing and Structural Stability, 49
D. The Hartman Grobman Theorem, 51
E. Smale s Horseshoe Map and Symbolic Dynamics, 54
F. Hyperbolic Invariant Sets, 58
G. Trellis Structure and Resonance Zones, 59
xii CONTENTS
H. Topological Entropy, 70
I. Problems, 71
J. Further Reading, 72
4 Isolated Invariant Sets and Isolating Blocks, 73
A. Attracting Sets, 73
B. Isolated Invariant Sets and Isolating Blocks, 77
C. Constructing Isolating Blocks, 82
D. Basic Sets, 83
E. Symbolic Dynamics, 83
F. Filtrations of Isolated Invariant Sets, 85
G. Stacks of Isolating Blocks, 86
H. Calculating Directed Graphs, 88
I. Further Reading, 92
5 The Conley Index, 93
A. The Conley Index of an Isolating Block, 93
B. Continuation of Isolated Invariant Sets, 96
C. The Homology Conley Index, 98
D. References, 102
6 Symplectic Maps, 103
A. Linear Symplectic Maps, 103
B. Classical Mechanics, 107
C. Variational Principles, 110
D. Generating Functions, 113
E. Symplectic Integrators, 117
F. Separatrix Movement, 118
G. Normal Forms, 121
H. Problems, 125
I. Further Reading, 125
7 Invariant Measures, 126
A. Measure Spaces, 126
B. Invariant Measures, 127
C. Further Reading, 130
Appendix A Metric Spaces, 131
A. Definitions, 131
B. The Hausdorff Metric, 134
C. Fractals, 135
Appendix B Numerical Methods for Ordinary Differential Equations, 137
Appendix C Tangent Bundles, Manifolds, and Differential Forms, 142
PREFACE xiii
Appendix D Symplectic Manifolds, 147
Appendix E Algebraic Topology, 149
References, 152
Index, 155
|
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| id | DE-604.BV011906808 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:18:21Z |
| institution | BVB |
| isbn | 0195085450 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008047057 |
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| physical | XIII, 157 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | The Oxford engineering science series |
| series2 | The Oxford engineering science series |
| spelling | Easton, Robert W. Verfasser aut Geometric methods for discrete dynamical systems Robert W. Easton New York [u.a.] Oxford Univ. Press 1998 XIII, 157 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Oxford engineering science series 50 Dynamique différentiable ram Itération (mathématiques) ram Differentiable dynamical systems Iterative methods (Mathematics) Diskretes System (DE-588)4401225-1 gnd rswk-swf Diskretes System (DE-588)4401225-1 s DE-604 The Oxford engineering science series 50 (DE-604)BV001897240 50 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008047057&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Easton, Robert W. Geometric methods for discrete dynamical systems The Oxford engineering science series Dynamique différentiable ram Itération (mathématiques) ram Differentiable dynamical systems Iterative methods (Mathematics) Diskretes System (DE-588)4401225-1 gnd |
| subject_GND | (DE-588)4401225-1 |
| title | Geometric methods for discrete dynamical systems |
| title_auth | Geometric methods for discrete dynamical systems |
| title_exact_search | Geometric methods for discrete dynamical systems |
| title_full | Geometric methods for discrete dynamical systems Robert W. Easton |
| title_fullStr | Geometric methods for discrete dynamical systems Robert W. Easton |
| title_full_unstemmed | Geometric methods for discrete dynamical systems Robert W. Easton |
| title_short | Geometric methods for discrete dynamical systems |
| title_sort | geometric methods for discrete dynamical systems |
| topic | Dynamique différentiable ram Itération (mathématiques) ram Differentiable dynamical systems Iterative methods (Mathematics) Diskretes System (DE-588)4401225-1 gnd |
| topic_facet | Dynamique différentiable Itération (mathématiques) Differentiable dynamical systems Iterative methods (Mathematics) Diskretes System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008047057&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001897240 |
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