Global dynamics, phase space transport, orbits homoclinic to resonances, and applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[1993]
|
| Series: | Fields Institute for Research in Mathematical Sciences: Fields Institute monographs
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Vorwort: "This monograph consists of a series of weekly lectures that I gave at the Fields Institute during January through March of 1993." |
| Physical Description: | xi, 155 Seiten Diagramme |
| ISBN: | 0821892029 9780821892022 |
Staff View
MARC
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| 245 | 1 | 0 | |a Global dynamics, phase space transport, orbits homoclinic to resonances, and applications |c Stephen Wiggins |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1993] | |
| 264 | 4 | |c © 1993 | |
| 300 | |a xi, 155 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Fields Institute for Research in Mathematical Sciences: Fields Institute monographs |v 1 | |
| 500 | |a Aus dem Vorwort: "This monograph consists of a series of weekly lectures that I gave at the Fields Institute during January through March of 1993." | ||
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 0 | 7 | |a Globale Analysis |0 (DE-588)4021285-3 |2 gnd |9 rswk-swf |
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Record in the Search Index
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Contents
List of Figures vii
Preface xi
1. Introduction 1
2. Homoclinic Tangles and Transport in Two Dimensional,
Time Periodic Vector Fields 7
2.1 Introduction 7
2.2 Melnikov's Method for Time Periodically Forced One
Degree of Freedom Hamiltonian Systems 7
2.3 Dynamics in Homoclinic Tangles 12
3. Transport in Cellular Flows 19
4. Homoclinic Tangles and Transport in Two Dimensional,
Time Quasiperiodic Vector Fields 29
4.1 Introduction 29
4.2 Melnikov's Method for Two Dimensional Quasiperiodically
Time Dependent Vector Fields 29
4.3 The Geometry of Manifold Intersections 33
4.4 Lobes and Flux 35
5. Phase Space Transport in the Quasiperiodically Forced
Morse Oscillator 47
5.1 Introduction 47
5.2 The Morse Oscillator 47
5.3 Set Up of the Transport Problem 50
5.4 Fluxes and Dissociation rates 52
6. Adiabatic Dynamical Systems 57
7. Transport in the Eccentric Journal Bearing Flow: An Application
of Adiabatic Dynamical Systems 63
7.1 Introduction 63
7.2 The Eccentric Journal Bearing Flow 63
V
vi CONTENTS
7.3 Transport Analysis Lobe Geometry and Dynamics 69
7.4 Analytical Estimates from Adiabatic Dynamical Systems Theory . . 78
8. Orbits Homoclinic to Resonances: Global Analysis and Geometric
Singular Perturbation Methods 81
8.1 The Basic Perturbed, Two Degree of Freedom Integrable Hamilto
nian System 81
8.2 The Analytic and Geometric Structure of the Unperturbed
Equations 82
8.2.1 The Dynamics of the Unperturbed System Restricted to M. . 83
8.2.2 The Dynamics in F and its Relation to the Dynamics in M. . 83
8.3 The Analytic and Geometric Structure of the Perturbed Equations . 84
8.3.1 The Persistence of M and its Stable and Unstable Manifolds 84
8.3.2 The Dynamics on Aie near the Resonance 88
8.3.3 The Fibering of Ws(Ae) and Wtt{Ae) The Singular Pertur¬
bation Nature 98
8.4 Melnikov's Method for Detecting Orbits Homoclinic and Heteroclinic
to Invariant Sets in Ac 103
8.5 An Example: Dynamics of a Modal Truncation of the Nonlinear
Schrodinger Equation 126
8.5.1 The Unperturbed Structure 129
8.5.2 The Perturbed Structure 133
8.5.3 Orbits Homoclinic to pe: Non Hamiltonian Perturbations . . 140
8.5.4 Orbits Homoclinic to qe: Non Hamiltonian Perturbations . . 141
8.5.5 Orbits Homoclinic to Internal Orbits: Hamiltonian Pertur¬
bations 143
References 147
Index 153 |
| any_adam_object | 1 |
| author | Wiggins, Stephen ca. 20./21. Jh |
| author_GND | (DE-588)1247764664 |
| author_facet | Wiggins, Stephen ca. 20./21. Jh |
| author_role | aut |
| author_sort | Wiggins, Stephen ca. 20./21. Jh |
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| dewey-ones | 514 - Topology |
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| discipline | Mathematik |
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| id | DE-604.BV009743781 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-20T00:34:27Z |
| institution | BVB |
| isbn | 0821892029 9780821892022 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006444207 |
| oclc_num | 29222473 |
| open_access_boolean | |
| owner | DE-12 DE-188 |
| owner_facet | DE-12 DE-188 |
| physical | xi, 155 Seiten Diagramme |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Fields Institute for Research in Mathematical Sciences: Fields Institute monographs |
| series2 | Fields Institute for Research in Mathematical Sciences: Fields Institute monographs |
| spelling | Wiggins, Stephen ca. 20./21. Jh. Verfasser (DE-588)1247764664 aut Global dynamics, phase space transport, orbits homoclinic to resonances, and applications Stephen Wiggins Providence, Rhode Island American Mathematical Society [1993] © 1993 xi, 155 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Fields Institute for Research in Mathematical Sciences: Fields Institute monographs 1 Aus dem Vorwort: "This monograph consists of a series of weekly lectures that I gave at the Fields Institute during January through March of 1993." Differentiable dynamical systems Global analysis (Mathematics) Globale Analysis (DE-588)4021285-3 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Globale Analysis (DE-588)4021285-3 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-3128-0 Fields Institute for Research in Mathematical Sciences: Fields Institute monographs 1 (DE-604)BV009737926 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006444207&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wiggins, Stephen ca. 20./21. Jh Global dynamics, phase space transport, orbits homoclinic to resonances, and applications Fields Institute for Research in Mathematical Sciences: Fields Institute monographs Differentiable dynamical systems Global analysis (Mathematics) Globale Analysis (DE-588)4021285-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4021285-3 (DE-588)4137931-7 |
| title | Global dynamics, phase space transport, orbits homoclinic to resonances, and applications |
| title_auth | Global dynamics, phase space transport, orbits homoclinic to resonances, and applications |
| title_exact_search | Global dynamics, phase space transport, orbits homoclinic to resonances, and applications |
| title_full | Global dynamics, phase space transport, orbits homoclinic to resonances, and applications Stephen Wiggins |
| title_fullStr | Global dynamics, phase space transport, orbits homoclinic to resonances, and applications Stephen Wiggins |
| title_full_unstemmed | Global dynamics, phase space transport, orbits homoclinic to resonances, and applications Stephen Wiggins |
| title_short | Global dynamics, phase space transport, orbits homoclinic to resonances, and applications |
| title_sort | global dynamics phase space transport orbits homoclinic to resonances and applications |
| topic | Differentiable dynamical systems Global analysis (Mathematics) Globale Analysis (DE-588)4021285-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Differentiable dynamical systems Global analysis (Mathematics) Globale Analysis Differenzierbares dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006444207&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009737926 |
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