Topological dynamics and ordinary differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
London [u.a.]
Van Nostrand Reinhold
1971
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Van Nostrand Reinhold mathematical studies
33 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 199 S. |
| ISBN: | 0442075022 |
Internformat
MARC
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| 245 | 1 | 0 | |a Topological dynamics and ordinary differential equations |c George R. Sell |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a London [u.a.] |b Van Nostrand Reinhold |c 1971 | |
| 300 | |a IX, 199 S. | ||
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| 650 | 4 | |a Dynamique topologique | |
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| 650 | 4 | |a Topological dynamics | |
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Datensatz im Suchindex
| _version_ | 1804117291932057600 |
|---|---|
| adam_text | CONTENTS
Preface v
Chapter I. Review of Uniform Spaces
I. A Generalized sequences 1
I. B Iterated limits 3
I. C Uniform topologies 4
I. D Linear topological spaces 7
I. E Examples 8
Chapter II. Basic Properties of Dynamical Systems
II. A Flows and semi flows 11
II.B An important example 13
II. C Modified definition of a flow 14
II. D Limit sets and compact motions 18
II. E Minimal sets 22
II. F Semi flows, revisited 23
II. G Attractors 23
Chapter III. Examples of Flows and Semi flows
III. A Autonomous differential equations 27
III. B Nonautonomous differential equations ... 28
III. C Parametric equations 28
III. D Difference equations 29
III. E Continuous functions ,.. 29
III. F Sequences 34
III. G Bounded uniformly continuous functions ... 35
III. H Bounded sequenced 35
III. I Continuous functions with parameters 36
III. J Sequences with parameters 38
viii CONTENTS
III. K Markov chains 39
III. L Measurable functions 39
III. M The space HjR, # ) 44
III. N Measurable functions with parameters 48
III. 0 Two parameter functions 54
Chapter IV. Nonautonomous Differential Equations
IV. A The basic construction 59
IV. B The extension problem 61
IV. C Compact solutions 62
IV. D Limiting equations 65
IV. E Discontinuous differential equations 66
IV. F Abstract formulation for n (x, i, t) 68
Chapter V. Almost Periodic Functions
V. A Definition of almost periodicity 71
V. B Properties of almost periodic functions .... 72
V. C Almost periodic functions in linear spaces . 78
V. D An inportant example 82
Chapter VI. Recurrent Motions and Almost Periodic Motions
VI. A Poisson stability 85
VI. B Recurrence 90
VI. C Almost periodic motions 94
VI. D Kakutani Baum theorem 106
Chapter VII. The Structure of o Limit Sets
VII. A Minimal case 113
VII. B A. p. minimal case 114
VII. C Periodic minimal case 116
VII. D An example 119
CONTENTS ix
Chapter VIII. Applications to Differential Equations
VIII. A The solution 0 (x, /, t) and the motion
n{x,t,t) 123
VIII. B Structure of limiting equations 125
VIII. C Stability 129
VIII. D Existence of periodic and almost periodic
solutions 138
VIII. E Behavior near an equilibrium point 143
Chapter IX. Invariant Measures
IX. A An example from classical mechanics 149
IX. B Invariant measures and Poisson stability 152
IX. C Existence of invariant measures 153
IX. D Examples of invariant measures 156
IX. E Nonautonomous differential equations 157
Chapter X. Ergodic Theory
X. A Birkhoff ergodic theorems 167
X. B Ergodic theory on W x H(f) 173
Chapter XI. Applications to Integral Equations
XI. A Volterra integral equations 177
XI. B Abstract formulation for n (/, g, a; t) 181
XI. C The mapping Tfi 182
XI. D. Limiting equations 183
XI. E. An application 186
Appendix A. Kamke s Lemma
A. 1 Compactness proof 189
A. 2 Differential inequality proof 190
References 193
Index 197
|
| any_adam_object | 1 |
| author | Sell, George R. 1937- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.3 |
| dewey-search | 514/.3 |
| dewey-sort | 3514 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV003002862 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:52:05Z |
| institution | BVB |
| isbn | 0442075022 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001879889 |
| oclc_num | 298410 |
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| owner | DE-384 DE-703 DE-355 DE-BY-UBR DE-20 DE-19 DE-BY-UBM DE-29T DE-188 |
| owner_facet | DE-384 DE-703 DE-355 DE-BY-UBR DE-20 DE-19 DE-BY-UBM DE-29T DE-188 |
| physical | IX, 199 S. |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Van Nostrand Reinhold |
| record_format | marc |
| series | Van Nostrand Reinhold mathematical studies |
| series2 | Van Nostrand Reinhold mathematical studies |
| spelling | Sell, George R. 1937- Verfasser (DE-588)172369576 aut Topological dynamics and ordinary differential equations George R. Sell 1. publ. London [u.a.] Van Nostrand Reinhold 1971 IX, 199 S. txt rdacontent n rdamedia nc rdacarrier Van Nostrand Reinhold mathematical studies 33 Dynamique topologique Topologische dynamica gtt Differential equations Topological dynamics Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Topologische Dynamik (DE-588)4253345-4 gnd rswk-swf Topologische Dynamik (DE-588)4253345-4 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Differentialgleichung (DE-588)4012249-9 s Van Nostrand Reinhold mathematical studies 33 (DE-604)BV002492122 33 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001879889&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sell, George R. 1937- Topological dynamics and ordinary differential equations Van Nostrand Reinhold mathematical studies Dynamique topologique Topologische dynamica gtt Differential equations Topological dynamics Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Topologische Dynamik (DE-588)4253345-4 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4020929-5 (DE-588)4253345-4 |
| title | Topological dynamics and ordinary differential equations |
| title_auth | Topological dynamics and ordinary differential equations |
| title_exact_search | Topological dynamics and ordinary differential equations |
| title_full | Topological dynamics and ordinary differential equations George R. Sell |
| title_fullStr | Topological dynamics and ordinary differential equations George R. Sell |
| title_full_unstemmed | Topological dynamics and ordinary differential equations George R. Sell |
| title_short | Topological dynamics and ordinary differential equations |
| title_sort | topological dynamics and ordinary differential equations |
| topic | Dynamique topologique Topologische dynamica gtt Differential equations Topological dynamics Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Topologische Dynamik (DE-588)4253345-4 gnd |
| topic_facet | Dynamique topologique Topologische dynamica Differential equations Topological dynamics Differentialgleichung Gewöhnliche Differentialgleichung Topologische Dynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001879889&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002492122 |
| work_keys_str_mv | AT sellgeorger topologicaldynamicsandordinarydifferentialequations |