Nonautonomous dynamical systems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2011
|
| Schriftenreihe: | Mathematical surveys and monographs
176 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | VIII, 264 S. graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Kloeden, Peter E. |d 1949- |e Verfasser |0 (DE-588)115479155 |4 aut | |
| 245 | 1 | 0 | |a Nonautonomous dynamical systems |c Peter E. Kloeden ; Martin Rasmussen |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2011 | |
| 300 | |a VIII, 264 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v 176 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Dynamics | |
| 650 | 4 | |a Ergodic theory | |
| 650 | 4 | |a Stability | |
| 650 | 7 | |a Dynamical systems and ergodic theory / Topological dynamics / Nonautonomous dynamical systems |2 msc | |
| 650 | 7 | |a Dynamical systems and ergodic theory / Smooth dynamical systems: general theory / Nonautonomous smooth dynamical systems |2 msc | |
| 650 | 7 | |a Dynamical systems and ergodic theory / Random dynamical systems / Foundations, general theory of cocycles, algebraic ergodic theory |2 msc | |
| 650 | 7 | |a Dynamical systems and ergodic theory / Topological dynamics / Lyapunov functions and stability; attractors, repellers |2 msc | |
| 650 | 7 | |a Dynamical systems and ergodic theory / Smooth dynamical systems: general theory / Stability theory |2 msc | |
| 650 | 7 | |a Dynamical systems and ergodic theory / Dynamical systems with hyperbolic behavior / Invariant manifold theory |2 msc | |
| 650 | 7 | |a Dynamical systems and ergodic theory / Local and nonlocal bifurcation theory / Attractors and their bifurcations |2 msc | |
| 650 | 0 | 7 | |a Ergodentheorie |0 (DE-588)4015246-7 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
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| 700 | 1 | |a Rasmussen, Martin |d 1975- |e Verfasser |0 (DE-588)132076349 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1403-0 |
| 830 | 0 | |a Mathematical surveys and monographs |v 176 |w (DE-604)BV000018014 |9 176 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024140203&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024140203 | ||
Datensatz im Suchindex
| _version_ | 1804147952695902208 |
|---|---|
| adam_text | Contents
Preface
Chapter
1.
Autonomous dynamical systems
1
1.
Introduction
1
2.
Local asymptotic behavior
4
3.
Global asymptotic behavior
12
4.
Dependence on parameters
17
Chapter
2.
Nonautonomous dynamical systems
23
1.
Processes formulation
23
2.
Skew product flow formulation
26
3.
Entire solutions and invariant sets
31
Chapter
3.
Attractors
37
1.
Attractors of processes
38
2.
Attractors of skew product flows
41
3.
Existence of pullback attractors
44
4.
Relationship between nonautonomous attractors
52
5.
Upper semi-continuous dependence on parameters
55
6.
Parametricallv inflated pullback attractors
57
7.
Pullback attractors with continuous fibers
60
8.
Local attractors and
repellere
62
Chapter
4.
Morse decompositions
69
1.
Attractor-repeller pairs
69
2.
Morse decompositions
72
3.
The one-dimensional case
75
Chapter
5.
Linear systems
79
1.
Exponential dichotomy
79
2.
Dichotomy spectrum
82
3.
Lyapunov spectrum
87
4.
Morse decompositions
89
Chapter
6.
Invariant manifolds
105
1.
Global invariant manifolds
105
2.
Local invariant manifolds
112
3.
Hierarchies of invariant manifolds
114
4.
Taylor approximation
116
5.
Reduction principle
123
v¡
CONTENTS
Chapter
7.
Lyapunov functions
129
1.
Lyapunov functions for solutions
129
2.
Lyapunov functions for autonomous attractors
132
3.
Lyapunov functions for pullback attractors
135
4.
Lyapunov functions for Morse decompositions
143
Chapter
8.
Bifurcations
147
1.
Nonautonomous Bernoulli equations
147
2.
One-dimensional bifurcation patterns
149
3.
Higher-dimensional Bernoulli-like equations
157
4.
Further developments
163
Chapter
9.
Set-valued nonautonomous dynamical systems
169
1.
Set-valued processes
170
2.
Set-valued skew product flows
173
3.
Backward extension of autonomous semi-dynamical systems
175
4.
Proof of existence of nonautonomous invariant sets
178
Chapter
10.
Nonautonomous semi-dynamical systems
185
1.
Attractors of skew product semi-flows
185
2.
The twisted horseshoe mapping
189
Chapter
11.
Approximation and perturbation of attractors
191
1.
Nonautonomous perturbations of an autonomous system
191
2.
Numerical approximation of uniform attractors
193
3.
Perturbation of the driving system
197
Chapter
12.
Infinite-dimensional systems
205
1.
Squeezing and flattening properties: the autonomous case
205
2.
Pullback asymptotic compactness
207
Chapter
13.
Switching and control systems
213
1.
Switching systems
213
2. Affine
control systems
222
Chapter
14.
Random dynamical systems
227
1.
Random attractors
228
2.
The Ornstein-Uhlenbeck process
229
3.
Random attractors for stochastic differential equations
231
Chapter
15.
Synchronization
235
1.
Deterministic nonautonomous systems
235
2.
Synchronization of systems with additive noise
242
3.
Synchronization of systems with linear noise
247
Appendix
251
Bibliography
253
Index
263
|
| any_adam_object | 1 |
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| author_facet | Kloeden, Peter E. 1949- Rasmussen, Martin 1975- |
| author_role | aut aut |
| author_sort | Kloeden, Peter E. 1949- |
| author_variant | p e k pe pek m r mr |
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| bvnumber | BV039121635 |
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| dewey-full | 515/.392 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.392 |
| dewey-search | 515/.392 |
| dewey-sort | 3515 3392 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T23:59:25Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024140203 |
| oclc_num | 732967764 |
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| physical | VIII, 264 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Kloeden, Peter E. 1949- Verfasser (DE-588)115479155 aut Nonautonomous dynamical systems Peter E. Kloeden ; Martin Rasmussen Providence, RI American Math. Soc. 2011 VIII, 264 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 176 Includes bibliographical references and index Dynamics Ergodic theory Stability Dynamical systems and ergodic theory / Topological dynamics / Nonautonomous dynamical systems msc Dynamical systems and ergodic theory / Smooth dynamical systems: general theory / Nonautonomous smooth dynamical systems msc Dynamical systems and ergodic theory / Random dynamical systems / Foundations, general theory of cocycles, algebraic ergodic theory msc Dynamical systems and ergodic theory / Topological dynamics / Lyapunov functions and stability; attractors, repellers msc Dynamical systems and ergodic theory / Smooth dynamical systems: general theory / Stability theory msc Dynamical systems and ergodic theory / Dynamical systems with hyperbolic behavior / Invariant manifold theory msc Dynamical systems and ergodic theory / Local and nonlocal bifurcation theory / Attractors and their bifurcations msc Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s Dynamisches System (DE-588)4013396-5 s DE-604 Rasmussen, Martin 1975- Verfasser (DE-588)132076349 aut Erscheint auch als Online-Ausgabe 978-1-4704-1403-0 Mathematical surveys and monographs 176 (DE-604)BV000018014 176 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024140203&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kloeden, Peter E. 1949- Rasmussen, Martin 1975- Nonautonomous dynamical systems Mathematical surveys and monographs Dynamics Ergodic theory Stability Dynamical systems and ergodic theory / Topological dynamics / Nonautonomous dynamical systems msc Dynamical systems and ergodic theory / Smooth dynamical systems: general theory / Nonautonomous smooth dynamical systems msc Dynamical systems and ergodic theory / Random dynamical systems / Foundations, general theory of cocycles, algebraic ergodic theory msc Dynamical systems and ergodic theory / Topological dynamics / Lyapunov functions and stability; attractors, repellers msc Dynamical systems and ergodic theory / Smooth dynamical systems: general theory / Stability theory msc Dynamical systems and ergodic theory / Dynamical systems with hyperbolic behavior / Invariant manifold theory msc Dynamical systems and ergodic theory / Local and nonlocal bifurcation theory / Attractors and their bifurcations msc Ergodentheorie (DE-588)4015246-7 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4015246-7 (DE-588)4013396-5 |
| title | Nonautonomous dynamical systems |
| title_auth | Nonautonomous dynamical systems |
| title_exact_search | Nonautonomous dynamical systems |
| title_full | Nonautonomous dynamical systems Peter E. Kloeden ; Martin Rasmussen |
| title_fullStr | Nonautonomous dynamical systems Peter E. Kloeden ; Martin Rasmussen |
| title_full_unstemmed | Nonautonomous dynamical systems Peter E. Kloeden ; Martin Rasmussen |
| title_short | Nonautonomous dynamical systems |
| title_sort | nonautonomous dynamical systems |
| topic | Dynamics Ergodic theory Stability Dynamical systems and ergodic theory / Topological dynamics / Nonautonomous dynamical systems msc Dynamical systems and ergodic theory / Smooth dynamical systems: general theory / Nonautonomous smooth dynamical systems msc Dynamical systems and ergodic theory / Random dynamical systems / Foundations, general theory of cocycles, algebraic ergodic theory msc Dynamical systems and ergodic theory / Topological dynamics / Lyapunov functions and stability; attractors, repellers msc Dynamical systems and ergodic theory / Smooth dynamical systems: general theory / Stability theory msc Dynamical systems and ergodic theory / Dynamical systems with hyperbolic behavior / Invariant manifold theory msc Dynamical systems and ergodic theory / Local and nonlocal bifurcation theory / Attractors and their bifurcations msc Ergodentheorie (DE-588)4015246-7 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Dynamics Ergodic theory Stability Dynamical systems and ergodic theory / Topological dynamics / Nonautonomous dynamical systems Dynamical systems and ergodic theory / Smooth dynamical systems: general theory / Nonautonomous smooth dynamical systems Dynamical systems and ergodic theory / Random dynamical systems / Foundations, general theory of cocycles, algebraic ergodic theory Dynamical systems and ergodic theory / Topological dynamics / Lyapunov functions and stability; attractors, repellers Dynamical systems and ergodic theory / Smooth dynamical systems: general theory / Stability theory Dynamical systems and ergodic theory / Dynamical systems with hyperbolic behavior / Invariant manifold theory Dynamical systems and ergodic theory / Local and nonlocal bifurcation theory / Attractors and their bifurcations Ergodentheorie Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024140203&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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