Chaotic transport in dynamical systems
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1992
|
| Schriftenreihe: | Interdisciplinary applied mathematics
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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MARC
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| 100 | 1 | |a Wiggins, Stephen |d ca. 20./21. Jh. |e Verfasser |0 (DE-588)1247764664 |4 aut | |
| 245 | 1 | 0 | |a Chaotic transport in dynamical systems |c Stephen Wiggins |
| 264 | 1 | |a New York u.a. |b Springer |c 1992 | |
| 300 | |a XIII, 301 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Interdisciplinary applied mathematics |v 2 | |
| 650 | 7 | |a Comportement chaotique des systèmes |2 ram | |
| 650 | 7 | |a Systèmes dynamiques différentiables |2 ram | |
| 650 | 7 | |a Transport, théorie du |2 ram | |
| 650 | 4 | |a Chaotic behavior in systems | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Transport theory | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface vii
1 Introduction and Examples 1
Example 1.1 Uniform Elliptical Vortices in External,
Linear Time Dependent Velocity Fields. . 2
Example 1.2 Capture and Passage
Through Resonance in Celestial Mechanics 9
Example 1.3 Bubble Dynamics in Straining Flows ... 10
Example 1.4 Photodissociation of Molecules:
The Driven Morse Oscillator 13
2 Transport in Two Dimensional Maps: General Principles
and Results 17
2.1 Mathematical Framework and Definitions 18
2.2 Transport Across a Boundary 20
2.3 Statement of the General Transport Problem
and Some Results 29
2.4 Examples 38
Example 2.1 The Oscillating Vortex Pair Flow
Geometry 38
Example 2.2 The 1:1 Resonance or
Periodically Forced Pendulum Geometry . 44
Example 2.3 52
Example 2.4 53
2.5 Chaos 54
2.6 Melnikov s Method and Transport Issues 64
2.7 Special Results for Area Preserving Maps:
Quasiperiodic Orbits 73
2.8 Nonhyperbolicity 79
3 Convective Mixing and Transport Problems
in Fluid Mechanics 81
3.1 The Oscillating Vortex Pair Flow 83
3.2 Two Dimensional, Time Periodic Rayleigh Benard
Convection 101
xii Contents
4 Transport in Quasiperiodically Forced Systems: Dynamics
Generated by Sequences of Maps 121
4.1 The Systems Under Consideration and Phase Space Geometry 123
4.2 The Quasiperiodic Melnikov Function 129
4.3 The Geometry of Ws{t€)C Wu{tc) and Lobes 132
4.4 Lobe Dynamics and Flux 142
4.5 Two Applications 166
4.6 The Nonautonomous System: Phase Space Structure for
Sequences of Maps 172
4.7 Numerical Simulations of Lobe Structures 176
4.8 Chaos 184
4.9 Final Remarks 190
5 Markov Models 193
5.1 Implementing the Markov Model and an Application to the
OVP Flow 193
5.2 Comparing the Markov Model with the Methods Developed
in Chapter 2 for Two Dimensional, Time Periodic Rayleigh
Benard Convection 197
5.3 Comparison of the MacKay, Meiss, Ott, and Percival
Markov Model with the Transport Theory of Rom Kedar
and Wiggins 202
6 Transport in fc Degree of Freedom Hamiltonian Systems,
3 k oo: The Generalization of Separatrices to Higher
Dimensions and Their Geometrical Structure 209
6.1 The Mathematical Framework for Transport in fc Degree
of Freedom Hamiltonian Systems, 3 fc oo 218
6.1.1 The Class of Perturbed, Integrable Hamiltonian
Systems under Consideration 218
6.1.2 The Geometric Structure of the Unperturbed Phase
Space 219
6.1.3 Reduction to a Poincare Map 228
6.1.4 The Geometric Structure of the Perturbed Phase
Space 230
6.2 Existence of Transverse Homoclinic and Heteroclinic
Manifolds: The Higher Dimensional Melnikov Theory . . . 232
6.3 An Example 235
6.4 Transport Near Resonances 249
6.4.1 Single Resonances 250
6.4.2 Higher Order Terms in the Normal Form 256
6.4.3 Single Resonance in 3 d.o.f. Systems 257
6.4.4 Nonisolation of Resonances: Resonance Channels . 260
6.4.5 Multiple Resonances 261
6.4.6 Resonance of Multiplicity 2 in 3 d.o.f. Systems . . . 264
Contents xiii
6.5 The Relationship to Arnold Diffusion 267
6.6 On the Advantage of Considering Near Integrable Systems 269
6.7 Final Remarks 270
Appendix 1 Proofs of Theorems 2.6 and 2.12 273
Appendix 2 Derivation of the Quasiperiodic Melnikov
Functions from Chapter 4 285
References 290
Index 297
|
| 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 |
| author_variant | s w sw |
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| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV004837707 |
| illustrated | Illustrated |
| indexdate | 2025-02-03T16:44:36Z |
| institution | BVB |
| isbn | 0387975225 3540975225 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002978660 |
| oclc_num | 24792948 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-739 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-703 DE-29T DE-19 DE-BY-UBM DE-634 DE-83 DE-188 |
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| physical | XIII, 301 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Springer |
| record_format | marc |
| series | Interdisciplinary applied mathematics |
| series2 | Interdisciplinary applied mathematics |
| spellingShingle | Wiggins, Stephen ca. 20./21. Jh Chaotic transport in dynamical systems Interdisciplinary applied mathematics Comportement chaotique des systèmes ram Systèmes dynamiques différentiables ram Transport, théorie du ram Chaotic behavior in systems Differentiable dynamical systems Transport theory Transporttheorie (DE-588)4185936-4 gnd Transportprozess (DE-588)4185932-7 gnd Dynamisches System (DE-588)4013396-5 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Chaos (DE-588)4191419-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4185936-4 (DE-588)4185932-7 (DE-588)4013396-5 (DE-588)4126142-2 (DE-588)4191419-3 (DE-588)4137931-7 (DE-588)4316104-2 |
| title | Chaotic transport in dynamical systems |
| title_auth | Chaotic transport in dynamical systems |
| title_exact_search | Chaotic transport in dynamical systems |
| title_full | Chaotic transport in dynamical systems Stephen Wiggins |
| title_fullStr | Chaotic transport in dynamical systems Stephen Wiggins |
| title_full_unstemmed | Chaotic transport in dynamical systems Stephen Wiggins |
| title_short | Chaotic transport in dynamical systems |
| title_sort | chaotic transport in dynamical systems |
| topic | Comportement chaotique des systèmes ram Systèmes dynamiques différentiables ram Transport, théorie du ram Chaotic behavior in systems Differentiable dynamical systems Transport theory Transporttheorie (DE-588)4185936-4 gnd Transportprozess (DE-588)4185932-7 gnd Dynamisches System (DE-588)4013396-5 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Chaos (DE-588)4191419-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Comportement chaotique des systèmes Systèmes dynamiques différentiables Transport, théorie du Chaotic behavior in systems Differentiable dynamical systems Transport theory Transporttheorie Transportprozess Dynamisches System Nichtlineares dynamisches System Chaos Differenzierbares dynamisches System Chaotisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002978660&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004216726 |
| work_keys_str_mv | AT wigginsstephen chaotictransportindynamicalsystems |