Topics in bifurcation theory and applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1992
|
| Schriftenreihe: | Advanced series in nonlinear dynamics
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 160 S. graph. Darst. |
| ISBN: | 9810210094 |
Internformat
MARC
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| 100 | 1 | |a Iooss, Gérard |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Topics in bifurcation theory and applications |c Gérard Iooss ; Moritz Adelmeyer |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1992 | |
| 300 | |a 160 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Advanced series in nonlinear dynamics |v 3 | |
| 650 | 7 | |a Bifurcatie |2 gtt | |
| 650 | 7 | |a Bifurcation, théorie de la |2 ram | |
| 650 | 7 | |a Differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Manifolds |2 gtt | |
| 650 | 7 | |a Niet-lineaire dynamica |2 gtt | |
| 650 | 4 | |a Bifurcation theory | |
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| 830 | 0 | |a Advanced series in nonlinear dynamics |v 3 |w (DE-604)BV004464593 |9 3 | |
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Datensatz im Suchindex
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| adam_text | Contents
Introduction 1
I Center Manifolds, Normal Forms, and Bifurcations of Vector Fields
near Critical Points 4
1.1 Unperturbed Vector Fields 4
1.1.1 Linearization 5
1.1.2 Center Manifold Theorem 7
1.1.3 Normal Form Theorem 12
1.1.4 Symmetries 22
1.1.5 Additional Examples and Exercises 25
Bibliographical Notes 31
1.2 Perturbed Vector Fields 31
1.2.1 Center Manifold and Normal Form Theorem for Perturbed
Vector Fields 32
1.2.2 Saddle Node and Pitchfork Bifurcation 37
1.2.3 Hopf Bifurcation 41
1.2.4 Hopf Bifurcation with S0(2) Symmetry 46
1.2.5 Steady Bifurcation with O(2) Symmetry 47
1.2.6 Hopf Bifurcation with 0(2) Symmetry 49
1.2.7 Exercises with Reversible Vector Fields 58
Appendix to Chapter I. Three Problems 62
Problem 1. The Lorenz System 62
Problem 2. The Van der Pol System 64
Problem 3. The Swift Hohenberg System 65
Answers to Problem 1 70
Answers to Problem 2 76
Answers to Problem 3 80
[I Couette Taylor Problem 88
II. 1 Formulation of the Problem 88
II. 1.1 Basic Equations 90
II.1.2 Symmetries 90
11.2 Couette Flow 91
11.3 Bifurcations from Couette Flow 92
11.3.1 Reformulation of the Problem 92
11.3.2 Axial Periodicity Condition 94
11.3.3 Stability of Couette Flow 95
11.3.4 Steady Bifurcation from Couette Flow: Taylor Vortex Flow . . 96
11.3.5 Hopf Bifurcation from Couette Flow: Spirals and Ribbons . . 99
11.4 Bifurcations from Taylor Vortex Flow 101
11.4.1 Center Manifold Reduction for Group Orbits of Steady Solutions 101
11.4.2 Steady Bifurcation from Taylor Vortices 103
11.4.3 Hopf Bifurcation from Taylor Vortices: Twisted Vortices, Wavy
Vortices, Vortices with Wavy Inflow and Outflow Boundaries . 107
III Center Manifolds, Normal Forms, and Bifurcations of Vector Fields
near Closed Orbits 111
111.1 Preliminaries. Adaptation of Floquet Theory 112
111.2 Unperturbed Case 123
111.2.1 Normal Form Theorem I 124
111.2.2 Normal Form Theorem II 133
111.2.3 Normal Form Theorem III 137
111.2.4 Additional Symmetries 140
111.3 Perturbed Case 143
111.3.1 Normal Form Theorems for the Perturbed Case 143
111.3.2 Saddle Node Bifurcation from Periodic Solutions 144
111.3.3 Pitchfork Bifurcation from Periodic Solutions 146
111.3.4 Hopf Bifurcation from Periodic Solutions (Part One) 148
111.3.5 Period Doubling Bifurcation 149
111.3.6 Hopf Bifurcation from Periodic Solutions (Part Two). Arnold s
Tongues 151
References 157
|
| any_adam_object | 1 |
| author | Iooss, Gérard Adelmeyer, Moritz |
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| discipline | Mathematik |
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| id | DE-604.BV006162884 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:41:23Z |
| institution | BVB |
| isbn | 9810210094 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003899619 |
| oclc_num | 25711966 |
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| physical | 160 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | World Scientific |
| record_format | marc |
| series | Advanced series in nonlinear dynamics |
| series2 | Advanced series in nonlinear dynamics |
| spelling | Iooss, Gérard Verfasser aut Topics in bifurcation theory and applications Gérard Iooss ; Moritz Adelmeyer Singapore [u.a.] World Scientific 1992 160 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advanced series in nonlinear dynamics 3 Bifurcatie gtt Bifurcation, théorie de la ram Differentiaalvergelijkingen gtt Manifolds gtt Niet-lineaire dynamica gtt Bifurcation theory Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 s DE-604 Adelmeyer, Moritz Verfasser (DE-588)122229584 aut Advanced series in nonlinear dynamics 3 (DE-604)BV004464593 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003899619&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Iooss, Gérard Adelmeyer, Moritz Topics in bifurcation theory and applications Advanced series in nonlinear dynamics Bifurcatie gtt Bifurcation, théorie de la ram Differentiaalvergelijkingen gtt Manifolds gtt Niet-lineaire dynamica gtt Bifurcation theory Verzweigung Mathematik (DE-588)4078889-1 gnd |
| subject_GND | (DE-588)4078889-1 |
| title | Topics in bifurcation theory and applications |
| title_auth | Topics in bifurcation theory and applications |
| title_exact_search | Topics in bifurcation theory and applications |
| title_full | Topics in bifurcation theory and applications Gérard Iooss ; Moritz Adelmeyer |
| title_fullStr | Topics in bifurcation theory and applications Gérard Iooss ; Moritz Adelmeyer |
| title_full_unstemmed | Topics in bifurcation theory and applications Gérard Iooss ; Moritz Adelmeyer |
| title_short | Topics in bifurcation theory and applications |
| title_sort | topics in bifurcation theory and applications |
| topic | Bifurcatie gtt Bifurcation, théorie de la ram Differentiaalvergelijkingen gtt Manifolds gtt Niet-lineaire dynamica gtt Bifurcation theory Verzweigung Mathematik (DE-588)4078889-1 gnd |
| topic_facet | Bifurcatie Bifurcation, théorie de la Differentiaalvergelijkingen Manifolds Niet-lineaire dynamica Bifurcation theory Verzweigung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003899619&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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