Lectures on bifurcations, dynamics and symmetry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow, Essex
Longman
1996
|
| Edition: | 1. publ. |
| Series: | Pitman research notes in mathematics series
356 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 159 S. graph. Darst. |
| ISBN: | 058230346X |
Staff View
MARC
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| 100 | 1 | |a Field, Michael |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lectures on bifurcations, dynamics and symmetry |c Michael Field |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow, Essex |b Longman |c 1996 | |
| 300 | |a 159 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Introduction k preliminaries 1
1. Introduction: Solving symmetric equations 1
2. Preliminaries 5
3. Invariants and Equivariants 9
Chapter 2. Hyperoctahedral groups 11
1. Finite reflection groups 11
2. The hyperoctahedral groups Cn 12
3. Invariants and equivariants for the hyperoctahedral group 15
4. Subgroups of the hyperoctahedral groups 17
5. Extensions and relations to wreath products 20
Chapter 3. A zoo of bifurcations 25
1. Bifurcation theory for Cn 25
2. Bifurcation theory for subgroups of Cn 26
Chapter 4. Stability and determinacy 32
1. Normal forms 32
2. Blowing up 34
3. The phase vector field 37
4. Stabilities 38
5. Higher order terms 40
6. A genericity theorem 42
7. Branching patterns, stability and determinacy 45
8. Location of equilibria 48
Chapter 5. The invariant sphere theorem 50
1. Asymptotics 50
2. The Invariant Sphere Theorem 51
Chapter 6. Heteroclinic cycles in equivariant bifurcations 58
1. Degenerate intersections forced by symmetry 58
2. The examples of dos Reis and Guckenheimer k Holmes 59
3. The representation (R4, A4 x Z4) 63
4. What is a heteroclinic cycle? 66
5. Notation and computations for general F = An m Zn 71
6. The representation (R5,A5 x Z5) 73
7. Subcycles 75
8. An example of a bifurcation to a heteroclmic cycle. 76
9. An asymptotically stable heteroclinic cycle 78
Chapter 7. Symmetrically coupled cell systems 81
1. Coupled cell systems 81
2. A model system of three cells 84
3. Edge cycles 91
4. Face cycles 94
Chapter 8. An example of Z2 transversality in a system of four coupled
oscillators 101
1. Stratumwise transversality 101
2. Equivariant transversality 102
3. A special case of Z2 transversality 103
4. Z2 equivariant dynamics 106
5. A Z2 transversal intersection between limit cycles 109
6. The coupled system {Oi,O2} 111
7. The coupled system {Oi,O3} 114
8. The coupled system {Oi,O2,O3,O4} 116
9. Speculations on global dynamics 119
Chapter 9. Geometric methods 122
1. Preliminaries 122
2. A class of equations 122
3. A factorization lemma 124
4. Stratifications 126
5. Stratifying the universal variety £ 129
6. Normalized families 131
7. Applications to equivariant bifurcation theory 132
8. Symmetry breaking isotropy types 135
9. Equivariant transversality 137
Appendix A. Converse to the MISC 139
1. Introduction 139
2. The counterexamples of Melbourne 139
3. A permutation representation on R4 141
4. The representation (V, F) 142
5. Equilibria 147
6. Dynamics 147
Hints and solutions to selected exercises 151
Bibliography 153
Index 156
|
| any_adam_object | 1 |
| author | Field, Michael |
| author_facet | Field, Michael |
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| ctrlnum | (OCoLC)35910702 (DE-599)BVBBV011124330 |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV011124330 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:04:23Z |
| institution | BVB |
| isbn | 058230346X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007453793 |
| oclc_num | 35910702 |
| open_access_boolean | |
| owner | DE-12 DE-11 DE-188 |
| owner_facet | DE-12 DE-11 DE-188 |
| physical | 159 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Longman |
| record_format | marc |
| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Field, Michael Verfasser aut Lectures on bifurcations, dynamics and symmetry Michael Field 1. publ. Harlow, Essex Longman 1996 159 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 356 Bifurcatie gtt Bifurcation theory Dynamics Symmetrie (DE-588)4058724-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Symmetrie (DE-588)4058724-1 s Verzweigung Mathematik (DE-588)4078889-1 s DE-604 Pitman research notes in mathematics series 356 (DE-604)BV000022845 356 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007453793&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Field, Michael Lectures on bifurcations, dynamics and symmetry Pitman research notes in mathematics series Bifurcatie gtt Bifurcation theory Dynamics Symmetrie (DE-588)4058724-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd |
| subject_GND | (DE-588)4058724-1 (DE-588)4012249-9 (DE-588)4078889-1 |
| title | Lectures on bifurcations, dynamics and symmetry |
| title_auth | Lectures on bifurcations, dynamics and symmetry |
| title_exact_search | Lectures on bifurcations, dynamics and symmetry |
| title_full | Lectures on bifurcations, dynamics and symmetry Michael Field |
| title_fullStr | Lectures on bifurcations, dynamics and symmetry Michael Field |
| title_full_unstemmed | Lectures on bifurcations, dynamics and symmetry Michael Field |
| title_short | Lectures on bifurcations, dynamics and symmetry |
| title_sort | lectures on bifurcations dynamics and symmetry |
| topic | Bifurcatie gtt Bifurcation theory Dynamics Symmetrie (DE-588)4058724-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd |
| topic_facet | Bifurcatie Bifurcation theory Dynamics Symmetrie Differentialgleichung Verzweigung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007453793&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022845 |
| work_keys_str_mv | AT fieldmichael lecturesonbifurcationsdynamicsandsymmetry |