Six lectures on dynamical systems:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1996
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 312 S. graph. Darst. |
| ISBN: | 9810225482 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | IMAGE 1
SIX LECTURES ON
DYNAMICAL SYSTEMS
EDITORS
B. AULBACH & F. COLONIUS INSTITUT FUER MATHEMATIK UNIVERSITAET AUGSBURG
GERMANY
^
^ WORLD SCIENTIFIC SINGAPORE * NEW JERSEY * LONDON * HONG KONG
IMAGE 2
CONTENTS
PREFACE V
DYNAMICAL SYSTEMS: THE TOPOLOGICAL FOUNDATIONS
BY FFLHAN AKIN
1 INTRODUCTION: DISCRETE TIME DYNAMICS AND CLOSED RELATIONS 1
2 RECURRENCE FOR CLOSED RELATIONS 7
3 INVARIANT SETS AND LYAPUNOV FUNCTIONS 14
4 ATTRACTORS AND BASIC SETS 24
5 MAPS BETWEEN DYNAMICAL SYSTEMS 33
BIBLIOGRAPHY 42
INTEGRAL MANIFOLDS FOR CARATHEODORY TYPE
DIFFERENTIAL EQUATIONS IN BANACH SPACES
BY BERND AULBACH AND THOMAS WANNER
1 PROLOGUE 45
2 BASIC DEFINITIONS AND RESULTS 48
3 QUASIBOUNDED SOLUTIONS 60
4 THE FUNDAMENTAL EXISTENCE THEOREM FOR INTEGRAL MANIFOLDS 76
5 HIERARCHIES OF INTEGRAL MANIFOLDS 90
6 THE CLASSICAL FIVE INTEGRAL MANIFOLDS 97
7 THE MISSING SIXTH INTEGRAL MANIFOLD 106
8 EPILOGUE 109
APPENDICES 110
A STRONG MEASURABILITY AND THE BOCHNER INTEGRAL 110
B BANACH S FIXED POINT THEOREM AND RELATED RESULTS 114
REFERENCES 117
VII
IMAGE 3
VIII CONTENTS
CONTROL THEORY AND DYNAMICAL SYSTEMS
BY FRITZ COLONIUS AND WOLFGANG KLIEMANN
1 INTRODUCTION 121
2 CONTROL SYSTEMS AS DYNAMICAL SYSTEMS 125
3 LIMIT BEHAVIOR OF CONTROLLED TRAJECTORIES 131
4 TWO PERTURBATION THEOREMS FOR ORDINAXY DIFFERENTIAL EQUATIONS 134
5 TWO EXAMPLES 139
6 ANALYSIS OF LINEARIZED CONTROL SYSTEMS 144
7 SPECTRAL THEORY OF NONLINEAR CONTROL SYSTEMS 150
REFERENCES 156
SHADOWING IN DISCRETE DYNAMICAL SYSTEMS
BY BRIAN A. COOMES, HUESEYIN KOGAK AND KENNETH J. PALMER
1 INTRODUCTION 163
2 THE INFINITE-TIME SHADOWING THEOREM 165
3 FINITE-TIME SHADOWING 175
3.1 THE FINITE-TIME SHADOWING THEOREM 175
3.2 IMPLEMENTATION OF THE THEOREM IN DIMENSION ONE 177
3.3 EXAMPLE: THE LOGISTIC MAP 181
3.4 IMPLEMENTATION OF THE THEOREM IN DIMENSION TWO 182
3.5 EXAMPLE: TINKERBELL MAP 188
4 PERIODIC SHADOWING 190
4.1 PERIODIC SHADOWING THEOREM 190
4.2 NECESSARY AND SUFFICIENT CONDITION THAT L _1 EXISTS 193
4.3 IMPLEMENTATION OF THE THEOREM IN DIMENSION ONE 194
4.4 EXAMPLE: THE LOGISTIC MAP 196
4.5 IMPLEMENTATION OF THE THEOREM IN DIMENSION TWO 196
4.6 EXAMPLE: THE HENON MAP 201
4.7 LYAPUNOV EXPONENTS FOR PERIODIC ORBITS OF MAPS 201
4.8 EXAMPLE: THE HENON MAP 208
REFERENCES 208
IMAGE 4
CONTENTS IX
PERTURBATIONS OF INVARIANT MANIFOLDS OF
ORDINARY DIFFERENTIAL EQUATIONS
BY GEORGE OSIPENKO AND EUGENE ERSHOV
1 INTRODUCTION 213
2 BASIC NOTIONS AND MOTIVATIONAL EXAMPLES 216
3 PERTURBATION OF EQUILIBRIA 223
4 INVARIANT MANIFOLDS OF PSEUDO-HYPERBOLIC LINEAR MAPS 231
5 PERTURBATION OF INVARIANT MANIFOLDS THROUGH AN EQUILIBRIUM 245
6 PERTURBATION OF PERIODIC ORBITS AND INVARIANT MANIFOLDS THROUGH THEM .
251
7 SACKER-NEIMARK AND MARIE THEOREMS 254
8 LOCALLY NON-UNIQUE INVARIANT MANIFOLDS 258
REFERENCES 263
THE REDUCTION OF DISCRETE DYNAMICAL AND
SEMIDYNAMICAL SYSTEMS IN METRIE SPACES
BY ANDREJS REINFELDS
1 INTRODUCTION 267
2 PRELIMINARIES 268
3 AUXILIARY LEMMAS 270
4 FIXED POINT 273
5 INVARIANT SETS 274
6 CONJUGACY OF HOMEOMORPHISMS 1 281
7 CONJUGACY OF NONINVERTIBLE MAPPINGS 290
8 CONJUGACY OF HOMEOMORPHISMS 2 293
9 APPLICATION TO STABILITY THEORY 304
10 SHADOWING LEMMA 305
REFERENCES 308
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| genre_facet | Aufsatzsammlung Konferenzschrift 1994 Augsburg |
| id | DE-604.BV011247434 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:06:30Z |
| institution | BVB |
| isbn | 9810225482 |
| language | English |
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| physical | IX, 312 S. graph. Darst. |
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| publisher | World Scientific |
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| spelling | Six lectures on dynamical systems ed. B. Aulbach ... Dynamical systems Singapore [u.a.] World Scientific 1996 IX, 312 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Commande, Théorie de la ram Dynamique différentiable ram Perturbation variété invariante Système dynamique discret Systèmes dynamiques ram Variété intégrale Differentiable dynamical systems Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content (DE-588)1071861417 Konferenzschrift 1994 Augsburg gnd-content Dynamisches System (DE-588)4013396-5 s DE-604 Differenzierbares dynamisches System (DE-588)4137931-7 s Aulbach, Bernd 1947-2005 Sonstige (DE-588)108857212 oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007549450&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Six lectures on dynamical systems Commande, Théorie de la ram Dynamique différentiable ram Perturbation variété invariante Système dynamique discret Systèmes dynamiques ram Variété intégrale Differentiable dynamical systems Differenzierbares dynamisches System (DE-588)4137931-7 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4137931-7 (DE-588)4013396-5 (DE-588)4143413-4 (DE-588)1071861417 |
| title | Six lectures on dynamical systems |
| title_alt | Dynamical systems |
| title_auth | Six lectures on dynamical systems |
| title_exact_search | Six lectures on dynamical systems |
| title_full | Six lectures on dynamical systems ed. B. Aulbach ... |
| title_fullStr | Six lectures on dynamical systems ed. B. Aulbach ... |
| title_full_unstemmed | Six lectures on dynamical systems ed. B. Aulbach ... |
| title_short | Six lectures on dynamical systems |
| title_sort | six lectures on dynamical systems |
| topic | Commande, Théorie de la ram Dynamique différentiable ram Perturbation variété invariante Système dynamique discret Systèmes dynamiques ram Variété intégrale Differentiable dynamical systems Differenzierbares dynamisches System (DE-588)4137931-7 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Commande, Théorie de la Dynamique différentiable Perturbation variété invariante Système dynamique discret Systèmes dynamiques Variété intégrale Differentiable dynamical systems Differenzierbares dynamisches System Dynamisches System Aufsatzsammlung Konferenzschrift 1994 Augsburg |
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