Topological and symbolic dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Paris
Soc. Mathématique de France
2003
|
| Schriftenreihe: | Collection SMF
Cours spécialisés ; 11 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 315 S. graph. Darst. |
| ISBN: | 2856291430 |
Internformat
MARC
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| 245 | 1 | 0 | |a Topological and symbolic dynamics |c Petr Kůrka |
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Datensatz im Suchindex
| _version_ | 1804150032815882240 |
|---|---|
| adam_text | CONTENTS
Preface vii
1. Dynamical systems 1
1.1. Differential equations 1
1.2. Flows and iterations 2
1.3. Fixed points and linearization 4
1.4. Quadratic system 7
1.5. Chaotic systems 13
1.6. Symbolic dynamics 17
1.7. Feigenbaum system 20
1.8. Dyadic adding machine 27
1.9. Covers and itineraries 29
1.10. Feigenbaum subshift 32
1.11. Rotations 34
1.12. Spiral phyllotaxis 40
Exercises 44
2. Topological dynamics 45
2.1. Dynamical relations 46
2.2. Minimal and transitive systems 50
2.3. Shadowing property 53
2.4. Recurrence 55
2.5. Equicontinuity and sensitivity 60
2.6. Maximal equicontinuous factors 66
2.7. Spectral theory 71
2.8. Attractors 76
2.9. Chain-invariant sets 82
2.10. Topological entropy 87
2.11. Characteristics of recurrence and transition 95
2.12. Strictly ergodic systems 98
Exercises 101
3. Symbolic dynamics 103
3.1. Symbolic spaces 104
3.2. Symbolic extensions 108
vi CONTENTS
3.3. Subshifts 112
3.4. Topological entropy 116
3.5. Subshifts of finite type 120
3.6. Transition graphs and their matrices 123
3.7. Sofic subshifts 130
3.8. Two-sided subshifts 139
Exercises 142
4. Minimal symbolic systems 143
4.1. Adding machines 144
4.2. Substitutive subshifts 150
4.3. Decoding and recognizability 162
4.4. Sturmian subshifts 168
4.5. Skew Sturmian subshifts 179
4.6. Toeplitz subshifts 189
Exercises 201
5. Cellular automata 203
5.1. Equicontinuity 210
5.2. Surjectivity 214
5.3. Openness 222
5.4. Closingness 226
5.5. Expansivity 231
5.6. Attractors 233
5.7. Factor subshifts 238
5.8. Classification 244
Exercises 246
A. Sets, spaces and numbers 247
A. 1. Sets and relations 247
A.2. Metric spaces 249
A.3. Compact spaces 253
A.4. Connected spaces 261
A.5. Spaces of continuous functions 263
A.6. Topological spaces 266
A.7. Uniform spaces 274
A.8. Compact groups 277
A.9. Perron-Frobenius theory 280
A.10. Continued fractions 283
B. Main theorems 293
Bibliography 297
Notation 307
Index 311
|
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| id | DE-604.BV040722405 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:32:29Z |
| institution | BVB |
| isbn | 2856291430 |
| language | English |
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| publisher | Soc. Mathématique de France |
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| spelling | Kůrka, Petr Verfasser aut Topological and symbolic dynamics Petr Kůrka Paris Soc. Mathématique de France 2003 XII, 315 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Collection SMF : Cours spécialisés 11 Collection SMF Cours spécialisés ; 11 (DE-604)BV012699276 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025702584&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kůrka, Petr Topological and symbolic dynamics Collection SMF |
| title | Topological and symbolic dynamics |
| title_auth | Topological and symbolic dynamics |
| title_exact_search | Topological and symbolic dynamics |
| title_full | Topological and symbolic dynamics Petr Kůrka |
| title_fullStr | Topological and symbolic dynamics Petr Kůrka |
| title_full_unstemmed | Topological and symbolic dynamics Petr Kůrka |
| title_short | Topological and symbolic dynamics |
| title_sort | topological and symbolic dynamics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025702584&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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