Singularity theory and equivariant symplectic maps:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1993
|
| Schriftenreihe: | Lecture notes in mathematics
1558 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 226 S. graph. Darst. |
| ISBN: | 3540572961 0387572961 |
Internformat
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| 100 | 1 | |a Bridges, Thomas J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Singularity theory and equivariant symplectic maps |c Thomas J. Bridges ; Jacques E. Furter |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1993 | |
| 300 | |a VI, 226 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1558 | |
| 650 | 7 | |a Application symplectique équivariante |2 Jussieu | |
| 650 | 4 | |a Applications différentiables | |
| 650 | 7 | |a Bifurcation |2 Jussieu | |
| 650 | 4 | |a Bifurcation, Théorie de la | |
| 650 | 7 | |a Bifurcation, Théorie de la |2 ram | |
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| 650 | 7 | |a Gradient |2 Jussieu | |
| 650 | 7 | |a Manifolds |2 gtt | |
| 650 | 7 | |a Point périodique |2 Jussieu | |
| 650 | 7 | |a Singularité |2 Jussieu | |
| 650 | 4 | |a Singularités (Mathématiques) | |
| 650 | 7 | |a Singularités (mathématiques) |2 ram | |
| 650 | 7 | |a Symplectomorphisme |2 Jussieu | |
| 650 | 4 | |a Bifurcation theory | |
| 650 | 4 | |a Differentiable mappings | |
| 650 | 4 | |a Singularities (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1805082758287982592 |
|---|---|
| adam_text |
Table of Contents
1. Introduction 1
2. Generic bifurcation of periodic points 9
2.1 Lagrangian variational formulation 10
2.2 Linearization and unfolding 13
2.3 Symmetries 17
2.4 Normal form for bifurcating period q points 19
2.5 Reduced stability of bifurcating periodic points 23
2.6 4D symplectic maps and the collision singularity 27
3. Singularity theory for equivariant gradient bifurcation problems 33
3.1 Contact equivalence and gradient maps 35
3.2 Fundamental results 38
3.3 Potentials and paths 40
3.4 Equivalence for paths 43
3.5 Proofs 48
4. Classification of Z? equivariant gradient bifurcation problems 63
4.1 ^' classification of potentials 64
4.2 Classification of Z, equivariant bifurcation problems 69
4.3 Bifurcation diagrams for the unfolding (4.9) 74
5. Period 3 points of the generalized standard map 85
5.1 Computations of the bifurcation equation 86
5.2 Analysis of the bifurcation equations 87
6. Classification of D, equivariant gradient maps on R2 89
6.1 D9 normal forms when q / 4 89
6.2 D4 invariant potentials with a distinguished parameter path 90
7. Reversibility and degenerate bifurcation of period q points
of tnultiparameter maps 101
7.1 Period 3 points with reversibility in multiparameter maps 103
7.2 Period 4 points with reversibility in multiparameter maps 110
7.3 Generic period 5 points in the generalized standard map 116
8. Periodic points of equivariant symplectic maps 119
8.1 Subharmonic bifurcation in equivariant symplectic maps 121
VI
8.2 Subharmonic bifurcation when S acts absolutely irreducibly on R" 130
8.3 O(2) equivariant syraplectic maps 132
8.4 Parametrically forced spherical pendulum 140
8.5 Reduction to the orbit space '. 144
8.6 Remarks on linear stability for equivariant maps 146
9. Collision of multipliers at rational points for symplectic maps 149
9.1 Generic theory for nonlinear rational collision 150
9.2 Collision at third root of unity: 6 = 2tt/3 157
9.3 Collision of multipliers at ±i 160
9.4 Collision at rational points with q 5 165
9.5 Reduced instability for the bifurcating period ? points 166
9.6 Reduced stability for bifurcating period 4 points 168
9.7 Remarks on the collision at irrational points 171
10. Equivariant maps and the collision of multipliers 175
10.1 Reversible symplectic maps on R4 176
10.2 Symplectic maps on R4 with spatial symmetry .179
Appendices 185
A. Equivariant Splitting Lemma 185
B. Signature on configuration space 185
C. Linear stability on configuration space 190
D. Transformation to linear normal form 192
E. Symmetries and conservation laws 194
F. About reversible symplectic maps 196
G. Twist maps and dynamical equivalence 199
H. Z, equivariant bifurcation equations and linear stability 200
I. About symmetric symplectic operators 202
J. (p, ^ resonances for symplectic maps 205
K. About reversible equivariant symplectic maps 209
L. Bifurcations and critical points of equivariant functionals 210
M. Instability Lemma 212
N. Isotropy and twisted subgroupsof S x Zg 213
References 215
Author Index 221
Subject Index 223 |
| any_adam_object | 1 |
| author | Bridges, Thomas J. Furter, Jacques E. |
| author_facet | Bridges, Thomas J. Furter, Jacques E. |
| author_role | aut aut |
| author_sort | Bridges, Thomas J. |
| author_variant | t j b tj tjb j e f je jef |
| building | Verbundindex |
| bvnumber | BV008220265 |
| callnumber-first | Q - Science |
| callnumber-label | QA613 |
| callnumber-raw | QA613.64 |
| callnumber-search | QA613.64 |
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 514/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.74 |
| dewey-search | 514/.74 |
| dewey-sort | 3514 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV008220265 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:37:45Z |
| institution | BVB |
| isbn | 3540572961 0387572961 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005426800 |
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| physical | VI, 226 S. graph. Darst. |
| publishDate | 1993 |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Bridges, Thomas J. Verfasser aut Singularity theory and equivariant symplectic maps Thomas J. Bridges ; Jacques E. Furter Berlin [u.a.] Springer 1993 VI, 226 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1558 Application symplectique équivariante Jussieu Applications différentiables Bifurcation Jussieu Bifurcation, Théorie de la Bifurcation, Théorie de la ram Gewone differentiaalvergelijkingen gtt Gradient Jussieu Manifolds gtt Point périodique Jussieu Singularité Jussieu Singularités (Mathématiques) Singularités (mathématiques) ram Symplectomorphisme Jussieu Bifurcation theory Differentiable mappings Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Äquivariante Abbildung (DE-588)4203527-2 gnd rswk-swf Symplektische Abbildung (DE-588)4332207-4 gnd rswk-swf Äquivariante Abbildung (DE-588)4203527-2 s Singularität Mathematik (DE-588)4077459-4 s DE-604 Symplektische Abbildung (DE-588)4332207-4 s Furter, Jacques E. Verfasser aut Lecture notes in mathematics 1558 (DE-604)BV000676446 1558 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005426800&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bridges, Thomas J. Furter, Jacques E. Singularity theory and equivariant symplectic maps Lecture notes in mathematics Application symplectique équivariante Jussieu Applications différentiables Bifurcation Jussieu Bifurcation, Théorie de la Bifurcation, Théorie de la ram Gewone differentiaalvergelijkingen gtt Gradient Jussieu Manifolds gtt Point périodique Jussieu Singularité Jussieu Singularités (Mathématiques) Singularités (mathématiques) ram Symplectomorphisme Jussieu Bifurcation theory Differentiable mappings Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd Äquivariante Abbildung (DE-588)4203527-2 gnd Symplektische Abbildung (DE-588)4332207-4 gnd |
| subject_GND | (DE-588)4077459-4 (DE-588)4203527-2 (DE-588)4332207-4 |
| title | Singularity theory and equivariant symplectic maps |
| title_auth | Singularity theory and equivariant symplectic maps |
| title_exact_search | Singularity theory and equivariant symplectic maps |
| title_full | Singularity theory and equivariant symplectic maps Thomas J. Bridges ; Jacques E. Furter |
| title_fullStr | Singularity theory and equivariant symplectic maps Thomas J. Bridges ; Jacques E. Furter |
| title_full_unstemmed | Singularity theory and equivariant symplectic maps Thomas J. Bridges ; Jacques E. Furter |
| title_short | Singularity theory and equivariant symplectic maps |
| title_sort | singularity theory and equivariant symplectic maps |
| topic | Application symplectique équivariante Jussieu Applications différentiables Bifurcation Jussieu Bifurcation, Théorie de la Bifurcation, Théorie de la ram Gewone differentiaalvergelijkingen gtt Gradient Jussieu Manifolds gtt Point périodique Jussieu Singularité Jussieu Singularités (Mathématiques) Singularités (mathématiques) ram Symplectomorphisme Jussieu Bifurcation theory Differentiable mappings Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd Äquivariante Abbildung (DE-588)4203527-2 gnd Symplektische Abbildung (DE-588)4332207-4 gnd |
| topic_facet | Application symplectique équivariante Applications différentiables Bifurcation Bifurcation, Théorie de la Gewone differentiaalvergelijkingen Gradient Manifolds Point périodique Singularité Singularités (Mathématiques) Singularités (mathématiques) Symplectomorphisme Bifurcation theory Differentiable mappings Singularities (Mathematics) Singularität Mathematik Äquivariante Abbildung Symplektische Abbildung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005426800&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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