Spaces of dynamical systems:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
De Gruyter
2012
|
| Series: | De Gruyter studies in mathematical physics
3 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XV, 229 S. graph. Darst. |
| ISBN: | 9783110258417 9783110255959 |
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| 240 | 1 | 0 | |a Prostranstva dinamicheskikh sistem |
| 245 | 1 | 0 | |a Spaces of dynamical systems |c Sergei Yu. Pilyugin |
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Record in the Search Index
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| adam_text |
Titel: Spaces of dynamical systems
Autor: Piljugin, Sergej Ju
Jahr: 2012
Vll
Contents
Preface
Nomenclature xi
1 Dynamical systems 1
1.1 Main definitions. 1
1.2 Embedding of a discrete dynamical system into a flow. 10
1.3 Local Poincare diffeomorphism. 11
1.4 Time-periodic systems of differential equations. 14
1.5 Action of an Abelian group. 15
2 Topologies on spaces of dynamical systems 16
2.1 C°-topology. 16
2.2 C'-topology. 17
2.3 Metrics on the space of systems of differential equations . 18
2.4 Generic properties. 24
2.5 Immersions and embeddings. 24
3 Equivalence relations 26
3.1 Topological conjugacy. 26
3.2 Topological equivalence of flows. 30
3.3 Nonwandering set. 30
3.4 Local equivalence. 36
4 Hyperbolic fixed point 37
4.1 Hyperbolic linear mapping. 37
4.2 The Grobman-Hartman theorem. 40
4.3 Neighborhood of a hyperbolic fixed point. 48
4.4 The stable manifold theorem. 53
4.5 Hyperbolic periodic point. 65
5 Hyperbolic rest point and hyperbolic closed trajectory 67
5.1 Hyperbolic rest point. 67
5.2 Hyperbolic closed trajectory. 72
xlv_Contents
6 Transversality 78
6.1 Transversality of mappings and submanifblds. 78
6.2 Transversality condition. 80
6.3 Palis lemma. 82
6.4 Transversality and hyperbolicity for one-dimensional mappings . 90
7 Hyperbolic sets 92
7.1 Definition of a hyperbolic set. 92
7.2 Examples of hyperbolic sets . 94
7.3 Basic properties of hyperbolic sets. 97
7.4 Stable manifold theorem. 101
7.5 Axiom A . 103
7.6 Hyperbolic sets of flows . 112
8 Anosov diffeomorphisms 119
9 Smale's horseshoe and chaos 126
9.1 Smale's horseshoe. 126
9.2 Chaotic sets. 131
9.3 Homoclinic points. 132
10 Closing Lemma 135
11 C°-generic properties of dynamical systems 141
11.1 Hausdorff metric . 141
11.2 Semicontinuous mappings. 142
11.3 Tolerance stability and Takens'theory. 143
11.4 Attractors of dynamical systems. 147
12 Shadowing of pseudotrajectories in dynamical systems 159
12.1 Definitions and results . 159
12.2 Proof of Theorem 12.1 . 164
12.3 Proof of Theorem 12.2. 172
12.4 Proof of Theorem 12.3. 175
A Scheme of the proof of the Mane theorem
181
B Lectures on the history of differential equations and dynamical systems 192
B.l Differential equations and Newton's anagram.192
B.2 Development of the general theory.194
Contents xv
B.3 Linear equations and systems. 198
B.4 Stability. 203
B.5 Nonlocal qualitative theory. Dynamical systems. 210
B.6 Structural stability. 214
B.7 Dynamical systems with chaotic behavior. 217
Bibliography 223
Index 227 |
| any_adam_object | 1 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.39 |
| dewey-search | 515.39 |
| dewey-sort | 3515.39 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| isbn | 9783110258417 9783110255959 |
| language | English |
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| physical | XV, 229 S. graph. Darst. |
| publishDate | 2012 |
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| publisher | De Gruyter |
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| series | De Gruyter studies in mathematical physics |
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| spelling | Piljugin, Sergej Ju. 1947- Verfasser (DE-588)121192865 aut Prostranstva dinamicheskikh sistem Spaces of dynamical systems Sergei Yu. Pilyugin Berlin De Gruyter 2012 XV, 229 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematical physics 3 Literaturangaben Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s DE-604 De Gruyter studies in mathematical physics 3 (DE-604)BV040141722 3 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3950674&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024998663&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Piljugin, Sergej Ju. 1947- Spaces of dynamical systems De Gruyter studies in mathematical physics Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4013396-5 |
| title | Spaces of dynamical systems |
| title_alt | Prostranstva dinamicheskikh sistem |
| title_auth | Spaces of dynamical systems |
| title_exact_search | Spaces of dynamical systems |
| title_full | Spaces of dynamical systems Sergei Yu. Pilyugin |
| title_fullStr | Spaces of dynamical systems Sergei Yu. Pilyugin |
| title_full_unstemmed | Spaces of dynamical systems Sergei Yu. Pilyugin |
| title_short | Spaces of dynamical systems |
| title_sort | spaces of dynamical systems |
| topic | Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Dynamisches System |
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