An Introduction to Infinite Dimensional Dynamical Systems — Geometric Theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1984
|
| Series: | Applied Mathematical Sciences
47 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The motivation for writing these notes came from a series of lectures of the third author on retarded functional differential equations at the Lefschetz Center for Dynamical Systems of the Division of Applied Mathematics at Brown University during the spring of 1982. Partial financial support was obtained from the Air Force Office of Scientific Research, AF-AFOSR 81- 0198, National Science Foundation, MCS 79-05774-05, U. S. Army Research Office, DAAG-29-79-C-016l, Instituto Nacional de Investiga~ao Cientifica, Portugal, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), Proc. No. 40. 3278/81, Fapesp and Reitoria da Universidade de Sao Paulo, Brasil. The authors appreciate the efforts of Dorothy Libutti, Katherine MacDougall, and Nancy Gancz for the preparation of the manuscript. Contents 1. Introduction 1 2. Retarded Functional Differential Equations on Manifolds 7 3. Examples of Retarded Functional Differential Equations on Manifolds 13 4. Generic Properties. The Theorem of Kupka-Smale 24 5. Invariant Sets, Limit Sets and the Attractor 43 6. The Dimension of the Attractor 56 7. Attractor Sets as Cl-Manifolds 69 8. Stability Relative to A(F) and Bifurcation 85 9. Cornpactification at Infinity 100 10. Stability of Morse-Smale Maps III 11. Bibliographical Notes 140 References 143 Appendix - An Introduction to Homotopy Index Theory in Noncornpact Spaces 147 References for Appendix 191 Subject Index 193 1 |
| Physical Description: | 1 Online-Ressource (VII, 196 p) |
| ISBN: | 9781475744934 9780387909318 |
| ISSN: | 0066-5452 |
| DOI: | 10.1007/978-1-4757-4493-4 |
Staff View
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| spelling | Hale, Jack K. Verfasser aut An Introduction to Infinite Dimensional Dynamical Systems — Geometric Theory by Jack K. Hale, Luis T. Magalhães, Waldyr M. Oliva Including: An Introduction to the Homotopy Theory in Noncompact Spaces New York, NY Springer New York 1984 1 Online-Ressource (VII, 196 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 47 0066-5452 The motivation for writing these notes came from a series of lectures of the third author on retarded functional differential equations at the Lefschetz Center for Dynamical Systems of the Division of Applied Mathematics at Brown University during the spring of 1982. Partial financial support was obtained from the Air Force Office of Scientific Research, AF-AFOSR 81- 0198, National Science Foundation, MCS 79-05774-05, U. S. Army Research Office, DAAG-29-79-C-016l, Instituto Nacional de Investiga~ao Cientifica, Portugal, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), Proc. No. 40. 3278/81, Fapesp and Reitoria da Universidade de Sao Paulo, Brasil. The authors appreciate the efforts of Dorothy Libutti, Katherine MacDougall, and Nancy Gancz for the preparation of the manuscript. Contents 1. Introduction 1 2. Retarded Functional Differential Equations on Manifolds 7 3. Examples of Retarded Functional Differential Equations on Manifolds 13 4. Generic Properties. The Theorem of Kupka-Smale 24 5. Invariant Sets, Limit Sets and the Attractor 43 6. The Dimension of the Attractor 56 7. Attractor Sets as Cl-Manifolds 69 8. Stability Relative to A(F) and Bifurcation 85 9. Cornpactification at Infinity 100 10. Stability of Morse-Smale Maps III 11. Bibliographical Notes 140 References 143 Appendix - An Introduction to Homotopy Index Theory in Noncornpact Spaces 147 References for Appendix 191 Subject Index 193 1 Mathematics Global analysis (Mathematics) Analysis Mathematik Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Unendlichdimensionales System (DE-588)4207956-1 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Retardierte Funktional-Differentialgleichung (DE-588)4609722-3 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Differentialgleichung (DE-588)4012249-9 s Mannigfaltigkeit (DE-588)4037379-4 s 1\p DE-604 Unendlichdimensionales System (DE-588)4207956-1 s 2\p DE-604 Retardierte Funktional-Differentialgleichung (DE-588)4609722-3 s 3\p DE-604 Differenzierbares dynamisches System (DE-588)4137931-7 s 4\p DE-604 Magalhães, Luis T. Sonstige oth Oliva, Waldyr M. Sonstige oth https://doi.org/10.1007/978-1-4757-4493-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hale, Jack K. An Introduction to Infinite Dimensional Dynamical Systems — Geometric Theory Mathematics Global analysis (Mathematics) Analysis Mathematik Mannigfaltigkeit (DE-588)4037379-4 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd Dynamisches System (DE-588)4013396-5 gnd Retardierte Funktional-Differentialgleichung (DE-588)4609722-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4137931-7 (DE-588)4207956-1 (DE-588)4013396-5 (DE-588)4609722-3 (DE-588)4012249-9 |
| title | An Introduction to Infinite Dimensional Dynamical Systems — Geometric Theory |
| title_alt | Including: An Introduction to the Homotopy Theory in Noncompact Spaces |
| title_auth | An Introduction to Infinite Dimensional Dynamical Systems — Geometric Theory |
| title_exact_search | An Introduction to Infinite Dimensional Dynamical Systems — Geometric Theory |
| title_full | An Introduction to Infinite Dimensional Dynamical Systems — Geometric Theory by Jack K. Hale, Luis T. Magalhães, Waldyr M. Oliva |
| title_fullStr | An Introduction to Infinite Dimensional Dynamical Systems — Geometric Theory by Jack K. Hale, Luis T. Magalhães, Waldyr M. Oliva |
| title_full_unstemmed | An Introduction to Infinite Dimensional Dynamical Systems — Geometric Theory by Jack K. Hale, Luis T. Magalhães, Waldyr M. Oliva |
| title_short | An Introduction to Infinite Dimensional Dynamical Systems — Geometric Theory |
| title_sort | an introduction to infinite dimensional dynamical systems geometric theory |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Mannigfaltigkeit (DE-588)4037379-4 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd Dynamisches System (DE-588)4013396-5 gnd Retardierte Funktional-Differentialgleichung (DE-588)4609722-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Mannigfaltigkeit Differenzierbares dynamisches System Unendlichdimensionales System Dynamisches System Retardierte Funktional-Differentialgleichung Differentialgleichung |
| url | https://doi.org/10.1007/978-1-4757-4493-4 |
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