Topological theory of dynamical systems: recent advances
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam u.a.
North-Holland
1994
|
| Series: | North-Holland mathematical library
52 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 416 S. |
| ISBN: | 0444899170 |
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| 100 | 1 | |a Aoki, Nobuo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Topological theory of dynamical systems |b recent advances |c N. Aoki ; K. Hiraide |
| 264 | 1 | |a Amsterdam u.a. |b North-Holland |c 1994 | |
| 300 | |a VIII, 416 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a Dynamique topologique |2 ram | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Topological dynamics | |
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Record in the Search Index
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| adam_text | CONTENTS
INTRODUCTION 1
CHAPTER 1 Some Properties of Anosov Systems 15
§1.1 Toral endomorphisms 15
§1.2 Anosov differentiable systems 19
CHAPTER 2 Dynamics of Continuous Maps 31
§2.1 Self covering maps 31
§2.2 Expansivity 36
§2.3 Pseudo orbit tracing property 78
§2.4 Topological Anosov maps (TA maps) 88
CHAPTER 3 Nonwandering Sets 96
§3.1 Chain recurrent sets 96
§3.2 Stable and unstable sets 102
§3.3 Recurrent sets and Birkhoff centers 107
§3.4 Nonwandering sets of TA maps 117
§3.5 Inverse limit systems 122
CHAPTER 4 Markov Partitions 127
§4.1 Markov partitions and subshifts 127
§4.2 Construction of Markov partitions 132
§4.3 Symbolic dynamics 140
CHAPTER 5 Local Product Structures 147
§5.1 Stable sets in strong sense 147
§5.2 Local product structures for TA covering maps 155
§5.3 Expanding factors of TA maps 162
§5.4 Subclasses of the class of TA maps 166
CHAPTER 6 TA Covering Maps 168
§6.1 Fundamental groups 168
§6.2 Universal covering spaces 174
§6.3 Covering transformation groups 182
§6.4 S injectivity of TA covering maps 189
§6.5 Structure groups for inverse limit systems 193
§6.6 Lifting of local product structures 203
§6.7 TA covering maps of closed topological manifolds 211
§6.8 Classification of TA covering maps on tori 219
vii
viii CONTENTS
CHAPTER 7 Solenoidal Groups and Self Covering Maps 222
§7.1 Geometrical structures of solenoidal groups 222
§7.2 Inverse limit systems of self covering maps on tori 231
CHAPTER 8 TA Covering Maps of Tori 241
§8.1 Toral endomorphisms homotopic to TA covering maps 241
§8.2 Construction of semi conjugacy maps 244
§8.3 Nonwandering sets 250
§8.4 Injectivity of semi conjugacy maps 257
§8.5 Proof of Theorem 6.8.1 268
§8.6 Proof of Theorem 6.8.2 269
§8.7 Remarks 275
CHAPTER 9 Perturbations of Hyperbolic Toral Endomorphisms • • ¦ 280
§9.1 TA C°° regular maps that are not Anosov 280
§9.2 One parameter families of homeomorphisms 288
CHAPTER 10 Fixed Point Indices 304
§10.1 Chain complexes 304
§10.2 Singular homology 310
§10.3 Euclidean neighborhood retracts (ENRs) 320
§10.4 Fixed point indices 326
§10.5 Lefschetz numbers 330
§10.6 Orientability of manifolds 332
§10.7 Orientability of generalized foliations 337
§10.8 Fixed point indices of expanding maps 346
§10.9 Fixed point indices of TA covering maps 348
CHAPTER 11 Foundations of Ergodic Theory 360
§11.1 Measure theory 360
§11.2 Measure preserving transformations 363
§11.3 Ergodic theorems 366
§11.4 Probability measures of compact metric spaces 375
§11.5 Applications to topological dynamics 387
REFERENCES 402
INDEX 411
|
| any_adam_object | 1 |
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| dewey-ones | 514 - Topology |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T17:40:05Z |
| institution | BVB |
| isbn | 0444899170 |
| language | English |
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| physical | VIII, 416 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | North-Holland |
| record_format | marc |
| series | North-Holland mathematical library |
| series2 | North-Holland mathematical library |
| spelling | Aoki, Nobuo Verfasser aut Topological theory of dynamical systems recent advances N. Aoki ; K. Hiraide Amsterdam u.a. North-Holland 1994 VIII, 416 S. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematical library 52 Dynamique différentiable ram Dynamique topologique ram Differentiable dynamical systems Topological dynamics Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Topologische Dynamik (DE-588)4253345-4 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Topologische Dynamik (DE-588)4253345-4 s DE-604 Hiraide, Kōichi Verfasser aut North-Holland mathematical library 52 (DE-604)BV000005206 52 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006442570&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aoki, Nobuo Hiraide, Kōichi Topological theory of dynamical systems recent advances North-Holland mathematical library Dynamique différentiable ram Dynamique topologique ram Differentiable dynamical systems Topological dynamics Differenzierbares dynamisches System (DE-588)4137931-7 gnd Topologische Dynamik (DE-588)4253345-4 gnd |
| subject_GND | (DE-588)4137931-7 (DE-588)4253345-4 |
| title | Topological theory of dynamical systems recent advances |
| title_auth | Topological theory of dynamical systems recent advances |
| title_exact_search | Topological theory of dynamical systems recent advances |
| title_full | Topological theory of dynamical systems recent advances N. Aoki ; K. Hiraide |
| title_fullStr | Topological theory of dynamical systems recent advances N. Aoki ; K. Hiraide |
| title_full_unstemmed | Topological theory of dynamical systems recent advances N. Aoki ; K. Hiraide |
| title_short | Topological theory of dynamical systems |
| title_sort | topological theory of dynamical systems recent advances |
| title_sub | recent advances |
| topic | Dynamique différentiable ram Dynamique topologique ram Differentiable dynamical systems Topological dynamics Differenzierbares dynamisches System (DE-588)4137931-7 gnd Topologische Dynamik (DE-588)4253345-4 gnd |
| topic_facet | Dynamique différentiable Dynamique topologique Differentiable dynamical systems Topological dynamics Differenzierbares dynamisches System Topologische Dynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006442570&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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