Dynamics in Infinite Dimensions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2002
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Applied Mathematical Sciences
47 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In our book published in 1984 An Introduction to Infinite Dimensional - namical Systems-Geometric Theory, we presented some aspects of a geometric theory of infinite dimensional spaces with major emphasis on retarded functional differential equations. In this book, the intent is the same. There are new results on Morse–Smale systems for semiflows, persistence of hyperbolicity under perturbations, nonuniform hyperbolicity, monotone dynamical systems, realization of vector fields on center manifolds and normal forms. In addition, more attention is devoted to neutral functional differential equations although the theory is much less developed. Some parts of the theory also will apply to many other types of equations and applications. Jack K. Hale Luis T. Magalh aes Waldyr M. Oliva Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Invariant Sets and Attractors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Functional Di?erential Equations on Manifolds . . . . . . . . . . . 19 3. 1 RFDE on manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3. 2 Examples of RFDE on manifolds . . . . . . . . . . . . . . . . . . . . . . . . . 29 3. 3 NFDE on manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 n 3. 4 NFDE on R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3. 4. 1 General properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3. 4. 2 Equivalence of point and compact dissipative . . . . . . . . 50 1 3. 5 An example of NFDE on S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3. 6 A canonical ODE in the Fr'echet category . . . . . . . . . . . . . . . . . . 54 4 The Dimension of the Attractor . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5 Stability and Bifurcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6 Stability of Morse–Smale Maps and Semiflows . . . . . . . . . . . . 81 6. 1 Morse–Smale maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6. 2 Morse–Smale semiflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6. 3 An example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7 One-to-Oneness, Persistence, and Hyperbolicity . . . . . . . . . |
| Beschreibung: | 1 Online-Ressource (VIII, 282 p) |
| ISBN: | 9780387228969 9781441930125 |
| DOI: | 10.1007/b100032 |
Internformat
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| 490 | 1 | |a Applied Mathematical Sciences |v 47 | |
| 500 | |a In our book published in 1984 An Introduction to Infinite Dimensional - namical Systems-Geometric Theory, we presented some aspects of a geometric theory of infinite dimensional spaces with major emphasis on retarded functional differential equations. In this book, the intent is the same. There are new results on Morse–Smale systems for semiflows, persistence of hyperbolicity under perturbations, nonuniform hyperbolicity, monotone dynamical systems, realization of vector fields on center manifolds and normal forms. In addition, more attention is devoted to neutral functional differential equations although the theory is much less developed. Some parts of the theory also will apply to many other types of equations and applications. Jack K. Hale Luis T. Magalh aes Waldyr M. Oliva Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | ||
| 500 | |a . . . . . . . . . . . . . 1 2 Invariant Sets and Attractors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Functional Di?erential Equations on Manifolds . . . . . . . . . . . 19 3. 1 RFDE on manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3. 2 Examples of RFDE on manifolds . . . . . . . . . . . . . . . . . . . . . . . . . 29 3. 3 NFDE on manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 n 3. 4 NFDE on R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3. 4. 1 General properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3. 4. 2 Equivalence of point and compact dissipative . . . . . . . . 50 1 3. 5 An example of NFDE on S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3. 6 A canonical ODE in the Fr'echet category . . . . . . . . . . . . . . . . . . 54 4 The Dimension of the Attractor . . . . . . . . . . . . . . . . . . . . . | ||
| 500 | |a . . . . . 57 5 Stability and Bifurcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6 Stability of Morse–Smale Maps and Semiflows . . . . . . . . . . . . 81 6. 1 Morse–Smale maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6. 2 Morse–Smale semiflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6. 3 An example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7 One-to-Oneness, Persistence, and Hyperbolicity . . . . . . . . . | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Global differential geometry | |
| 650 | 4 | |a Analysis | |
| 650 | 4 | |a Differential Geometry | |
| 650 | 4 | |a Mathematik | |
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Datensatz im Suchindex
| _version_ | 1804153089397096448 |
|---|---|
| any_adam_object | |
| author | Hale, Jack K. |
| author_facet | Hale, Jack K. |
| author_role | aut |
| author_sort | Hale, Jack K. |
| author_variant | j k h jk jkh |
| building | Verbundindex |
| bvnumber | BV042419128 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)704496231 (DE-599)BVBBV042419128 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/b100032 |
| edition | Second Edition |
| format | Electronic eBook |
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| id | DE-604.BV042419128 |
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| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9780387228969 9781441930125 |
| language | English |
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| series | Applied Mathematical Sciences |
| series2 | Applied Mathematical Sciences |
| spelling | Hale, Jack K. Verfasser aut Dynamics in Infinite Dimensions by Jack K. Hale, Luis T. Magalhães, Waldyr M. Oliva Second Edition New York, NY Springer New York 2002 1 Online-Ressource (VIII, 282 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 47 In our book published in 1984 An Introduction to Infinite Dimensional - namical Systems-Geometric Theory, we presented some aspects of a geometric theory of infinite dimensional spaces with major emphasis on retarded functional differential equations. In this book, the intent is the same. There are new results on Morse–Smale systems for semiflows, persistence of hyperbolicity under perturbations, nonuniform hyperbolicity, monotone dynamical systems, realization of vector fields on center manifolds and normal forms. In addition, more attention is devoted to neutral functional differential equations although the theory is much less developed. Some parts of the theory also will apply to many other types of equations and applications. Jack K. Hale Luis T. Magalh aes Waldyr M. Oliva Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Invariant Sets and Attractors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Functional Di?erential Equations on Manifolds . . . . . . . . . . . 19 3. 1 RFDE on manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3. 2 Examples of RFDE on manifolds . . . . . . . . . . . . . . . . . . . . . . . . . 29 3. 3 NFDE on manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 n 3. 4 NFDE on R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3. 4. 1 General properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3. 4. 2 Equivalence of point and compact dissipative . . . . . . . . 50 1 3. 5 An example of NFDE on S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3. 6 A canonical ODE in the Fr'echet category . . . . . . . . . . . . . . . . . . 54 4 The Dimension of the Attractor . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5 Stability and Bifurcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6 Stability of Morse–Smale Maps and Semiflows . . . . . . . . . . . . 81 6. 1 Morse–Smale maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6. 2 Morse–Smale semiflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6. 3 An example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7 One-to-Oneness, Persistence, and Hyperbolicity . . . . . . . . . Mathematics Global analysis (Mathematics) Global differential geometry Analysis Differential Geometry Mathematik 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 Dynamisches System (DE-588)4013396-5 s Unendlichdimensionales System (DE-588)4207956-1 s 1\p DE-604 Retardierte Funktional-Differentialgleichung (DE-588)4609722-3 s 2\p DE-604 Differenzierbares dynamisches System (DE-588)4137931-7 s 3\p DE-604 Magalhães, Luis T. Sonstige oth Oliva, Waldyr M. Sonstige oth Applied Mathematical Sciences 47 (DE-604)BV040244599 47 https://doi.org/10.1007/b100032 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 |
| spellingShingle | Hale, Jack K. Dynamics in Infinite Dimensions Applied Mathematical Sciences Mathematics Global analysis (Mathematics) Global differential geometry Analysis Differential Geometry Mathematik 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 |
| subject_GND | (DE-588)4137931-7 (DE-588)4207956-1 (DE-588)4013396-5 (DE-588)4609722-3 |
| title | Dynamics in Infinite Dimensions |
| title_auth | Dynamics in Infinite Dimensions |
| title_exact_search | Dynamics in Infinite Dimensions |
| title_full | Dynamics in Infinite Dimensions by Jack K. Hale, Luis T. Magalhães, Waldyr M. Oliva |
| title_fullStr | Dynamics in Infinite Dimensions by Jack K. Hale, Luis T. Magalhães, Waldyr M. Oliva |
| title_full_unstemmed | Dynamics in Infinite Dimensions by Jack K. Hale, Luis T. Magalhães, Waldyr M. Oliva |
| title_short | Dynamics in Infinite Dimensions |
| title_sort | dynamics in infinite dimensions |
| topic | Mathematics Global analysis (Mathematics) Global differential geometry Analysis Differential Geometry Mathematik 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 |
| topic_facet | Mathematics Global analysis (Mathematics) Global differential geometry Analysis Differential Geometry Mathematik Differenzierbares dynamisches System Unendlichdimensionales System Dynamisches System Retardierte Funktional-Differentialgleichung |
| url | https://doi.org/10.1007/b100032 |
| volume_link | (DE-604)BV040244599 |
| work_keys_str_mv | AT halejackk dynamicsininfinitedimensions AT magalhaesluist dynamicsininfinitedimensions AT olivawaldyrm dynamicsininfinitedimensions |