Topological dynamics of random dynamical systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1997
|
| Series: | Oxford mathematical monographs
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 203 S. |
| ISBN: | 0198501579 |
Staff View
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| 245 | 1 | 0 | |a Topological dynamics of random dynamical systems |c Nguyen Dinh Cong |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Introduction 1
1 Deterministic dynamical systems 5
1.1 Introduction 5
1.2 Equivalent dynamical systems 6
1.3 Structural stability and linearization 8
1.4 Classification 18
1.5 Other problems and discussion 20
2 Random dynamical systems: foundations 22
2.1 Introduction 22
2.2 The generation of random dynamical systems 25
2.2.1 Products of random mappings 25
2.2.2 Random differential equations 26
2.2.3 Stochastic differential equations 28
2.2.4 Local random dynamical systems 29
2.3 The multiplicative ergodic theorem of Oseledets 30
2.4 Lyapunov scalar products and Lyapunov norms 32
2.5 Some applications of random dynamical systems 41
2.5.1 Random Schrodinger operators 41
2.5.2 The noisy Duffing van der Pol oscillator 42
2.5.3 Structural dynamics in engineering 42
2.5.4 Population dynamics in biology 44
3 The linearization of nonlinear random dynamical
systems 46
3.1 Topological conjugacy of random dynamical systems 46
3.2 Exponential dichotomy 49
3.3 Random difference equations 50
3.4 The random Hartman Grobman theorem 61
3.5 Bifurcation theory 80
4 Topological classification of discrete time linear hy¬
perbolic cocycles 84
4.1 Introduction 84
4.2 Topological classification of periodic cocycles 87
4.3 Necessary conditions for topological conjugacy 92
4.4 Structural stability of contracting linear cocycles 100
4.5 Diagonalization of linear cocycles 104
viii CONTENTS
4.6 Classification of one dimensional linear hyperbolic cocy
cles 110
4.7 Classification of linear hyperbolic diagonal cocycles 112
4.8 A classification theorem 117
5 Structural stability of discrete time linear hyper¬
bolic cocycles 121
5.1 Introduction 121
5.2 Exponential dichotomy of a linear cocycle with respect to
a random norm 122
5.3 Structural stability of a linear cocycle having an exponen¬
tial dichotomy 123
5.4 Structural stability of linear hyperbolic cocycles 128
5.5 Applications 130
6 Structural stability of continuous time linear hyper¬
bolic cocycles 132
6.1 Introduction 132
6.2 Uniformly contracting and expanding cocycles 133
6.3 Non uniformly contracting and expanding linear cocycles 136
6.4 Structural stability 141
6.5 Application: the stability of deterministic hyperbolic sys¬
tems under small random noise 147
7 Topological classification of continuous time linear
hyperbolic cocycles 150
7.1 Introduction 150
7.2 Necessary conditions for topological conjugacy 151
7.3 Some orientation properties of linear hyperbolic cocycles 154
7.4 Topological classification 170
8 Topological invariants of linear cocycles 176
8.1 Introduction 176
8.2 Stable and unstable subspaces are topological invariants 177
8.3 When is the center subspace invariant? 186
Bibliography 190
Index 201
|
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| isbn | 0198501579 |
| language | English |
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| physical | VIII, 203 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
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| publisher | Clarendon Press |
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| series2 | Oxford mathematical monographs |
| spelling | Nguyen, Dinh-Cong Verfasser aut Topological dynamics of random dynamical systems Nguyen Dinh Cong Oxford Clarendon Press 1997 VIII, 203 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs PROCESSOS ESTOCASTICOS larpcal Topologische dynamica gtt Random dynamical systems Stochastic differential equations Topological dynamics Topologische Dynamik (DE-588)4253345-4 gnd rswk-swf Stochastisches dynamisches System (DE-588)4305316-6 gnd rswk-swf Stochastisches dynamisches System (DE-588)4305316-6 s Topologische Dynamik (DE-588)4253345-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007870078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nguyen, Dinh-Cong Topological dynamics of random dynamical systems PROCESSOS ESTOCASTICOS larpcal Topologische dynamica gtt Random dynamical systems Stochastic differential equations Topological dynamics Topologische Dynamik (DE-588)4253345-4 gnd Stochastisches dynamisches System (DE-588)4305316-6 gnd |
| subject_GND | (DE-588)4253345-4 (DE-588)4305316-6 |
| title | Topological dynamics of random dynamical systems |
| title_auth | Topological dynamics of random dynamical systems |
| title_exact_search | Topological dynamics of random dynamical systems |
| title_full | Topological dynamics of random dynamical systems Nguyen Dinh Cong |
| title_fullStr | Topological dynamics of random dynamical systems Nguyen Dinh Cong |
| title_full_unstemmed | Topological dynamics of random dynamical systems Nguyen Dinh Cong |
| title_short | Topological dynamics of random dynamical systems |
| title_sort | topological dynamics of random dynamical systems |
| topic | PROCESSOS ESTOCASTICOS larpcal Topologische dynamica gtt Random dynamical systems Stochastic differential equations Topological dynamics Topologische Dynamik (DE-588)4253345-4 gnd Stochastisches dynamisches System (DE-588)4305316-6 gnd |
| topic_facet | PROCESSOS ESTOCASTICOS Topologische dynamica Random dynamical systems Stochastic differential equations Topological dynamics Topologische Dynamik Stochastisches dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007870078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nguyendinhcong topologicaldynamicsofrandomdynamicalsystems |