Structures in dynamics: finite dimensional deterministic studies
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North-Holland
1991
|
| Schriftenreihe: | Studies in mathematical physics
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 309 S. graph. Darst. |
| ISBN: | 0444892575 0444892583 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | IMAGE 1
S T R U C T U R ES IN D Y N A M I CS
FINITE DIMENSIONAL DETERMINISTIC STUDIES
H.W. BROER
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF GRONINGEN GRONINGEN, THE
NETHERLANDS
F. DUMORTIER
DEPARTMENT OF MATHEMATICS, LIMBURGS UNIVERSITAIR CENTRUM DIEPENBEEK,
BELGIUM
S.J. VAN STRIEN
DEPARTMENT OF MATHEMATICS, POLYTECHNICAL UNIVERSITY OF DELFT DELFT, THE
NETHERLANDS
F. TAKENS
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF GRONINGEN GRONINGEN, THE
NETHERLANDS
NORTH-HOLLAND
IMAGE 2
CONTENTS
PREFACE V
1 INTRODUCTION TO DYNAMICAL SYSTEMS (H. W. BROER) 1
1.1 WHAT IS A DYNAMICAL SYSTEM? 2
1.2 SETTING OF THE PROBLEM 8
1.3 REFERENCES 22
2 GENERICITY AND STRUCTURAL STABILITY 25
(H. W. BROER & F. DUMORTIER)
2.1 PERSISTENCE, TOPOLOGY 25
2.2 EQUIVALENT DYNAMICS, STRUCTURAL STABILITY 26
2.3 IS STRUCTURAL STABILITY A GENERIC PROPERTY? 28
2.4 MISCELLANEOUS REMARKS 39
2.5 VECTOR FIELDS ON COMPACT SURFACES 45
2.6 REFERENCES 52
3 BIFURCATIONS (F. TAJCENS) 53
3.1 THE SADDLE NODE BIFURCATION 53
3.2 THE PERIOD DOUBLING BIFURCATION 63
3.3 THE HOPF BIFURCATION 69
3.4 FINAL REMARKS 76
3.5 REFERENCES 77
IMAGE 3
X CONTENTS
4 A FAMILY OF QUASI-PERIODIC ATTRACTORS (FF. W. BROER) 79
4.1 DEFINITION OF QUASI-PERIODICITY, SETTING OF THE PROBLEM 79
4.2 TWO EXAMPLES, A PRELIMINARY PERTURBATION ANALYSIS - 82
4.3 THE PERTURBATION PROBLEM FOR CIRCLE MAPS 85
4.4 SOME CONSERVATIVE REMARKS - 93
4.5 REFERENCES 94
5 CHAOS (F. TAKENS) 97
5.1 TIME SERIES 97
5.2 PREDICTION PROCEDURE 98
5.3 INTERPRETATION OF DIMENSION AND ENTROPY FOR DYNAMICAL SYSTEMS 101
5.4 ON THE DEFINITION OF CHAOS 106
5.5 CHAOS: PROBABILISTIC ASPECTS 108
5.5 REFERENCES 110
6 INTERVAL MAPS (S.J. V. STRIEN) 111
6.1 COMBINATORICS OF INTERVAL MAPS 112
6.2 TOPOLOGICAL PROPERTIES OF INTERVAL MAPS 132
6.3 METRIE AND STATISTICAL RESULTS 147
6.4 SOME FINAL REMARKS 158
6.5 REFERENCES 158
7 LOCAL STUDY OF PLANAR VECTOR FIELDS:
SINGULARITIES AND THEIR UNFOLDINGS (F. DUMORTIER) 161
7.1 INTRODUCTION 162
7.2 STUDY OF THE SINGULARITIES 167
7.3 VERSAL UNFOLDINGS FOR SINGULARITIES OF VECTOR FIELDS 169
7.4 REDUCTION TO THE CENTRE MANIFOLD 172
7.5 BLOWING UP 174
7.6 NORMAL FORMS 190
7.7 C-UNFOLDINGS ON R AND SEMI-HYPERBOLIC BIFURCATIONS ON R 2 204
IMAGE 4
CONTENTS
7.8 HOPF-TAKENS BIFURCATIONS ON R 2 210
7.9 SOME GLOBAL BIFURCATIONS OF CODIMENSION 1 ON THE PLANE - 219 7.10
THE BOGDANOV-TAKENS BIFURCATION 227
7.11 REFERENCES - 237
8 THE THERMODYNAMIC FORMALISM (F. TAKENS) 243
8.1 INVARIANT MEASURES FOR DYNAMICAL SYSTEMS 243
8.2 MEASURES DESCRIBING THERMODYNAMIC STATES 253
8.3 THE RUELLE OPERATOR 259
8.4 REFERENCES 265
9 CONSERVATIVE DYNAMICAL SYSTEMS (H. W. BROER) 267
9.1 INTRODUCTION 267
9.2 EXAMPLES OF INTEGRABLE SYSTEMS 269
9.3 HAMILTONIAN SYSTEMS 277
9.4 INTEGRABLE SYSTEMS 288
9.5 NEAR INTEGRABILITY 293
9.6 REFERENCES 301
SUBJECT INDEX 303
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| indexdate | 2024-07-09T16:18:08Z |
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| isbn | 0444892575 0444892583 |
| language | English |
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| physical | XI, 309 S. graph. Darst. |
| publishDate | 1991 |
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| series | Studies in mathematical physics |
| series2 | Studies in mathematical physics |
| spelling | Structures in dynamics finite dimensional deterministic studies H. W. Broer ... Amsterdam North-Holland 1991 XI, 309 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in mathematical physics 2 Chaos gtt Dynamique différentiable Dynamische systemen gtt Niet-lineaire dynamica gtt Differentiable dynamical systems Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Nichtlineares dynamisches System (DE-588)4126142-2 s DE-604 Broer, Hendrik W. 1950- Sonstige (DE-588)124653782 oth Studies in mathematical physics 2 (DE-604)BV004808178 2 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002965656&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Structures in dynamics finite dimensional deterministic studies Studies in mathematical physics Chaos gtt Dynamique différentiable Dynamische systemen gtt Niet-lineaire dynamica gtt Differentiable dynamical systems Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| subject_GND | (DE-588)4126142-2 (DE-588)4143413-4 |
| title | Structures in dynamics finite dimensional deterministic studies |
| title_auth | Structures in dynamics finite dimensional deterministic studies |
| title_exact_search | Structures in dynamics finite dimensional deterministic studies |
| title_full | Structures in dynamics finite dimensional deterministic studies H. W. Broer ... |
| title_fullStr | Structures in dynamics finite dimensional deterministic studies H. W. Broer ... |
| title_full_unstemmed | Structures in dynamics finite dimensional deterministic studies H. W. Broer ... |
| title_short | Structures in dynamics |
| title_sort | structures in dynamics finite dimensional deterministic studies |
| title_sub | finite dimensional deterministic studies |
| topic | Chaos gtt Dynamique différentiable Dynamische systemen gtt Niet-lineaire dynamica gtt Differentiable dynamical systems Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| topic_facet | Chaos Dynamique différentiable Dynamische systemen Niet-lineaire dynamica Differentiable dynamical systems Nichtlineares dynamisches System Aufsatzsammlung |
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