Normally Hyperbolic Invariant Manifolds in Dynamical Systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1994
|
| Schriftenreihe: | Applied Mathematical Sciences
105 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications |
| Beschreibung: | 1 Online-Ressource (IX, 194 p) |
| ISBN: | 9781461243120 9781461287346 |
| ISSN: | 0066-5452 |
| DOI: | 10.1007/978-1-4612-4312-0 |
Internformat
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| 490 | 0 | |a Applied Mathematical Sciences |v 105 |x 0066-5452 | |
| 500 | |a In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications | ||
| 650 | 4 | |a Mathematics | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Wiggins, Stephen ca. 20./21. Jh |
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| author_facet | Wiggins, Stephen ca. 20./21. Jh |
| author_role | aut |
| author_sort | Wiggins, Stephen ca. 20./21. Jh |
| author_variant | s w sw |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-4312-0 |
| format | Electronic eBook |
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| id | DE-604.BV042420269 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461243120 9781461287346 |
| issn | 0066-5452 |
| language | English |
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| physical | 1 Online-Ressource (IX, 194 p) |
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| publishDate | 1994 |
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| series2 | Applied Mathematical Sciences |
| spelling | Wiggins, Stephen ca. 20./21. Jh. Verfasser (DE-588)1247764664 aut Normally Hyperbolic Invariant Manifolds in Dynamical Systems by Stephen Wiggins New York, NY Springer New York 1994 1 Online-Ressource (IX, 194 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 105 0066-5452 In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications Mathematics Cell aggregation / Mathematics Mechanics Manifolds and Cell Complexes (incl. Diff.Topology) Statistical Physics, Dynamical Systems and Complexity Mathematik Dynamisches System (DE-588)4013396-5 gnd rswk-swf Invariante Mannigfaltigkeit (DE-588)4348147-4 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Invariante Mannigfaltigkeit (DE-588)4348147-4 s 1\p DE-604 https://doi.org/10.1007/978-1-4612-4312-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wiggins, Stephen ca. 20./21. Jh Normally Hyperbolic Invariant Manifolds in Dynamical Systems Mathematics Cell aggregation / Mathematics Mechanics Manifolds and Cell Complexes (incl. Diff.Topology) Statistical Physics, Dynamical Systems and Complexity Mathematik Dynamisches System (DE-588)4013396-5 gnd Invariante Mannigfaltigkeit (DE-588)4348147-4 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4348147-4 |
| title | Normally Hyperbolic Invariant Manifolds in Dynamical Systems |
| title_auth | Normally Hyperbolic Invariant Manifolds in Dynamical Systems |
| title_exact_search | Normally Hyperbolic Invariant Manifolds in Dynamical Systems |
| title_full | Normally Hyperbolic Invariant Manifolds in Dynamical Systems by Stephen Wiggins |
| title_fullStr | Normally Hyperbolic Invariant Manifolds in Dynamical Systems by Stephen Wiggins |
| title_full_unstemmed | Normally Hyperbolic Invariant Manifolds in Dynamical Systems by Stephen Wiggins |
| title_short | Normally Hyperbolic Invariant Manifolds in Dynamical Systems |
| title_sort | normally hyperbolic invariant manifolds in dynamical systems |
| topic | Mathematics Cell aggregation / Mathematics Mechanics Manifolds and Cell Complexes (incl. Diff.Topology) Statistical Physics, Dynamical Systems and Complexity Mathematik Dynamisches System (DE-588)4013396-5 gnd Invariante Mannigfaltigkeit (DE-588)4348147-4 gnd |
| topic_facet | Mathematics Cell aggregation / Mathematics Mechanics Manifolds and Cell Complexes (incl. Diff.Topology) Statistical Physics, Dynamical Systems and Complexity Mathematik Dynamisches System Invariante Mannigfaltigkeit |
| url | https://doi.org/10.1007/978-1-4612-4312-0 |
| work_keys_str_mv | AT wigginsstephen normallyhyperbolicinvariantmanifoldsindynamicalsystems |