Normal forms and bifurcation of planar vector fields:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Univ. Press
1994
|
| Edition: | 1. publ |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 472 S. graph. Darst. |
| ISBN: | 0521372267 |
Staff View
MARC
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| 245 | 1 | 0 | |a Normal forms and bifurcation of planar vector fields |c Shui-Nee Chow ; Chengzhi Li ; Duo Wang |
| 250 | |a 1. publ | ||
| 264 | 1 | |a Cambridge |b Univ. Press |c 1994 | |
| 300 | |a VIII, 472 S. |b graph. Darst. | ||
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| 650 | 7 | |a Bifurcation, théorie de la |2 ram | |
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| 650 | 7 | |a Vectorvelden |2 gtt | |
| 650 | 4 | |a Bifurcation theory | |
| 650 | 4 | |a Normal forms (Mathematics) | |
| 650 | 4 | |a Vector fields | |
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Record in the Search Index
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| adam_text | Contents
Preface page vii
Chapter 1 Center Manifolds 1
1.1 Existence and Uniqueness of Global Center
Manifolds 3
1.2 Smoothness of the Global Center Manifolds 12
1.3 Local Center Manifolds 27
1.4 Asymptotic Behavior and Invariant
Foliations 35
1.5 Bibliographical Notes 47
Chapter 2 Normal Forms 49
2.1 Normal Forms for Differential Equations
near a Critical Point 49
2.2 Poincare s Theorem and Siegel s Theorem 70
2.3 Normal Forms of Equations with Periodic
Coefficients 89
2.4 Normal Forms of Maps near a Fixed Point 98
2.5 Normal Forms of Equations with Symmetry 105
2.6 Normal Forms of Linear Hamiltonian
Systems 113
2.7 Normal Forms of Nonlinear Hamiltonian
Systems 122
2.8 Takens s Theorem 142
2.9 Versal Deformations of Matrices 148
2.10 Versal Deformations of Infinitesimally
Symplectic Matrices 162
2.11 Normal Forms with Codimension One
or Two 177
2.12 Bibliographical Notes 188
v
vi Contents
Chapter 3 Codimension One Bifurcations 191
3.1 Definitions and Jet Transversality Theorem 192
3.2 Bifurcation of Equilibria 197
3.3 Bifurcation of Homoclinic Orbits 213
3.4 Bibliographical Notes 226
Chapter 4 Codimension Two Bifurcations 228
4.1 Double Zero Eigenvalue 229
4.2 Double Zero Eigenvalue with Symmetry
of Order 2 259
4.3 Double Zero Eigenvalue with Symmetry
of Order 3 278
4.4 Double Zero Eigenvalue with Symmetry
of Order 4 292
4.5 Double Zero Eigenvalue with Symmetry
of Order 5 328
4.6 A Purely Imaginary Pair of Eigenvalues
and a Simple Zero Eigenvalue 335
4.7 Two Purely Imaginary Pairs of Eigenvalues 353
4.8 Bibliographical Notes 380
Chapter 5 Bifurcations with Codimension Higher
than Two 383
5.1 Hopf Bifurcation of Higher Order 383
5.2 Homoclinic Bifurcation of Higher Order 393
5.3 A Codimension 3 Bifurcation:
Cusp of Order 3 409
5.4 A Codimension 4 Bifurcation:
Cusp of Order 4 430
5.5 Bibliographical Notes 449
Bibliography 452
Index 469
|
| any_adam_object | 1 |
| author | Chow, Shui-Nee Li, Chengzhi Wang, Duo 1592-1652 |
| author_GND | (DE-588)133031136 (DE-588)120722917 |
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| author_sort | Chow, Shui-Nee |
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| discipline | Mathematik |
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| id | DE-604.BV009818252 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:41:26Z |
| institution | BVB |
| isbn | 0521372267 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006499710 |
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| physical | VIII, 472 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Univ. Press |
| record_format | marc |
| spelling | Chow, Shui-Nee Verfasser aut Normal forms and bifurcation of planar vector fields Shui-Nee Chow ; Chengzhi Li ; Duo Wang 1. publ Cambridge Univ. Press 1994 VIII, 472 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bifurcatie gtt Bifurcation, théorie de la ram Champs vectoriels ram Vectorvelden gtt Bifurcation theory Normal forms (Mathematics) Vector fields Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Planares Vektorfeld (DE-588)4261750-9 gnd rswk-swf Normalform (DE-588)4172025-8 gnd rswk-swf Planares Vektorfeld (DE-588)4261750-9 s Normalform (DE-588)4172025-8 s DE-604 Verzweigung Mathematik (DE-588)4078889-1 s Li, Chengzhi Verfasser (DE-588)133031136 aut Wang, Duo 1592-1652 Verfasser (DE-588)120722917 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006499710&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chow, Shui-Nee Li, Chengzhi Wang, Duo 1592-1652 Normal forms and bifurcation of planar vector fields Bifurcatie gtt Bifurcation, théorie de la ram Champs vectoriels ram Vectorvelden gtt Bifurcation theory Normal forms (Mathematics) Vector fields Verzweigung Mathematik (DE-588)4078889-1 gnd Planares Vektorfeld (DE-588)4261750-9 gnd Normalform (DE-588)4172025-8 gnd |
| subject_GND | (DE-588)4078889-1 (DE-588)4261750-9 (DE-588)4172025-8 |
| title | Normal forms and bifurcation of planar vector fields |
| title_auth | Normal forms and bifurcation of planar vector fields |
| title_exact_search | Normal forms and bifurcation of planar vector fields |
| title_full | Normal forms and bifurcation of planar vector fields Shui-Nee Chow ; Chengzhi Li ; Duo Wang |
| title_fullStr | Normal forms and bifurcation of planar vector fields Shui-Nee Chow ; Chengzhi Li ; Duo Wang |
| title_full_unstemmed | Normal forms and bifurcation of planar vector fields Shui-Nee Chow ; Chengzhi Li ; Duo Wang |
| title_short | Normal forms and bifurcation of planar vector fields |
| title_sort | normal forms and bifurcation of planar vector fields |
| topic | Bifurcatie gtt Bifurcation, théorie de la ram Champs vectoriels ram Vectorvelden gtt Bifurcation theory Normal forms (Mathematics) Vector fields Verzweigung Mathematik (DE-588)4078889-1 gnd Planares Vektorfeld (DE-588)4261750-9 gnd Normalform (DE-588)4172025-8 gnd |
| topic_facet | Bifurcatie Bifurcation, théorie de la Champs vectoriels Vectorvelden Bifurcation theory Normal forms (Mathematics) Vector fields Verzweigung Mathematik Planares Vektorfeld Normalform |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006499710&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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