Symmetry breaking for compact Lie groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1996
|
| Schriftenreihe: | American Mathematical Society: Memoirs of the American Mathematical Society
574 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Volume 120, Number 574 (second of 4 numbers) |
| Beschreibung: | VIII, 170 S. |
| ISBN: | 0821804359 |
Internformat
MARC
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| 300 | |a VIII, 170 S. | ||
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| 490 | 1 | |a American Mathematical Society: Memoirs of the American Mathematical Society |v 574 | |
| 500 | |a Volume 120, Number 574 (second of 4 numbers) | ||
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Datensatz im Suchindex
| _version_ | 1804125208815075328 |
|---|---|
| adam_text | Contents
1. Introduction 1
1.1. Notes for the reader 7
1.2. Acknowledgements 7
2. Technical Preliminaries and Basic Notations 8
2.1. F sets and isotropy types 8
2.2. Representations 8
2.3. Isotropy types for representations 10
2.4. Polynomial Invariants and Equivariants 10
2.5. Smooth families of equivariant maps 11
2.6. Normalized families 11
3. Branching and invariant group orbits 13
3.1. Relative equilibria and normal hyperbolicity 13
3.2. Branches of relative equilibria 17
3.3. The branching pattern 18
3.4. Stabilities 19
3.5. Branching conditions 19
3.6. The signed indexed branching pattern 20
3.7. Stable families 20
3.8. Determinacy 21
3.9. Strong determinacy 22
4. Genericity theorems 25
4.1. Semi algebraic and semi analytic sets 25
4.2. Invariant and equivariant generators 26
4.3. The variety E 26
4.4. Stability theorems I: Weak regularity 30
4.5. Stability theorems II: Regular families 34
4.6. Determinacy 41
4.7. Examples related to finite reflection groups 45
5. Finitely determined bifurcation problems I 47
5.1. The phase vector field 47
5.2. The spaces Ah{T, V), Bh{T,V) 49
5.3. Strong determinacy 54
6. Finitely determined bifurcation problems II 56
6.1. Statement of the main theorem 56
6.2. 2 stable relative equilibria 56
7. Strong determinacy: Technical preliminaries 62
7.1. Introduction 62
7.2. Notational conventions 62
7.3. Local geometry 63
7.4. Weakly regular families 65
7.5. Analytic families and solution branches 67
7.6. Compatible parametrizations and initial exponents 68
7.7. Remarks on the set £(f) 70
7.8. The parametrization theorem 70
vi Contents
7.9. The space U2 72
7.10. Initial exponents and the space T?.3 72
8. Strong determinacy: F finite 74
8.1. Analytic parametrizations 74
8.2. Estimates on eigenvalues 78
8.3. Fractional power series 79
8.4. Eigenvalue estimates: Analytic case 83
8.5. Eigenvalue estimates: Smooth case 84
8.6. Proof of Theorem 8.2.6 86
8.7. Strong determinacy: F finite 87
8.8. Formation of new branches under perturbation 88
9. Strong determinacy: F compact, non finite 89
9.1. Polar blowing up: Local theory 89
9.2. Polar blowing up: Global theory 91
9.3. Polar blowing up a F manifold 91
9.4. Blowing up 94
9.4.1. Blowing up along a linear subspace
9.4.2. Blowing up analytic varieties
9.4.3. Blowing up algebraic varieties
9.5. Conical sets 97
9.6. Algebraic and analytic structure of the orbit strata 97
9.7. Blowing up representations 99
9.7.1. Analytic theory
9.7.2. Algebraic theory
9.8. A tangent and normal decomposition 101
9.9. Blowing up arcs 103
9.10. Analytic parametrizations of solution branches 105
9.11. Lifting analytic parametrizations 106
9.12. Controlling the lifts of analytic parametrizations 107
9.13. Symmetric structure of parametrizations 107
9.14. An alternative proof of Proposition 9.13.2 109
9.15. Extensions of Proposition 9.13.2 111
9.16. Review and Summary of Notations 112
9.17. The exponent iA( ) 113
9.18. Estimates on eigenvalues 114
10. Proofs of the parametrization theorems 117
10.1. Resolution of singularities 117
10.2. Blowing up 118
10.3. Singular sets of real algebraic varieties 119
10.4. Embedded resolution of singularities 119
10.5. Blowing up embeddings 121
10.6. Blowing up £ 121
10.7. Reduction to a subspace of K,(F, V)N 125
10.8. Families of subspaces of VU{T, V)NR 127
10.9. Blowing up the maps Gq 128
10.10. Proof of Theorem 7.8.5 131
Contents vh
11. An application to the equivariant Hopf bifurcation 135
11.1. Limit cycles for equivariant flows 135
11.2. The equivariant Hopf bifurcation Fiedler s theorem 136
11.3. The equivariant Hopf bifurcation for F x 51 equivariant families 136
11.4. Completion of the proof of Theorem 11.2.1 138
A. Branches of relative equilibria 139
A.I. Introduction 139
A.2. Background on normal hyperbolicity 140
A.3. Branches of relative equilibria I 142
A.4. Horn neighborhoods I 143
A.5. Statement of the main Theorem 145
A.6. Lipschitz maps 146
A.7. Norm equivalences 146
A.8. Diffeomorphisms 147
A.9. Coordinates near a 148
A.10. Lipschitz sections of £ 150
A. 11. The graph transform 151
A. 11.1. The map / in pp coordinates
A.11.2. Invertibility of g
A. 11.3. Contractivity of /#
A. 11.4. Perturbation theory
A. 12. Horn neighborhoods II 155
A. 13. Vector space theory: Norm estimates in terms of eigenvalues 157
A.13.1. Hyperbolic linear maps
A. 13.2. Relatively hyperbolic families
A.14. Conditions (U) and (V) 162
A.15. Branches of relative equilibria II 163
A. 15.1. Standing assumptions
A.16. Proof of Theorem A.5.1 165
References 168
|
| any_adam_object | 1 |
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| bvnumber | BV010731206 |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010731206 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:57:55Z |
| institution | BVB |
| isbn | 0821804359 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007164431 |
| oclc_num | 440944537 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-384 DE-824 DE-12 DE-739 DE-29T DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-384 DE-824 DE-12 DE-739 DE-29T DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| physical | VIII, 170 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Field, Michael 1945- Verfasser (DE-588)131268996 aut Symmetry breaking for compact Lie groups Michael Field Providence, RI American Math. Soc. 1996 VIII, 170 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 574 Volume 120, Number 574 (second of 4 numbers) Geometrija - Diferencialna geometrija Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Kompakte Lie-Gruppe (DE-588)4164846-8 gnd rswk-swf Symmetriebrechung (DE-588)4184200-5 gnd rswk-swf Kompakte Lie-Gruppe (DE-588)4164846-8 s Symmetriebrechung (DE-588)4184200-5 s DE-604 Verzweigung Mathematik (DE-588)4078889-1 s American Mathematical Society: Memoirs of the American Mathematical Society 574 (DE-604)BV008000141 574 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007164431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Field, Michael 1945- Symmetry breaking for compact Lie groups American Mathematical Society: Memoirs of the American Mathematical Society Geometrija - Diferencialna geometrija Verzweigung Mathematik (DE-588)4078889-1 gnd Kompakte Lie-Gruppe (DE-588)4164846-8 gnd Symmetriebrechung (DE-588)4184200-5 gnd |
| subject_GND | (DE-588)4078889-1 (DE-588)4164846-8 (DE-588)4184200-5 |
| title | Symmetry breaking for compact Lie groups |
| title_auth | Symmetry breaking for compact Lie groups |
| title_exact_search | Symmetry breaking for compact Lie groups |
| title_full | Symmetry breaking for compact Lie groups Michael Field |
| title_fullStr | Symmetry breaking for compact Lie groups Michael Field |
| title_full_unstemmed | Symmetry breaking for compact Lie groups Michael Field |
| title_short | Symmetry breaking for compact Lie groups |
| title_sort | symmetry breaking for compact lie groups |
| topic | Geometrija - Diferencialna geometrija Verzweigung Mathematik (DE-588)4078889-1 gnd Kompakte Lie-Gruppe (DE-588)4164846-8 gnd Symmetriebrechung (DE-588)4184200-5 gnd |
| topic_facet | Geometrija - Diferencialna geometrija Verzweigung Mathematik Kompakte Lie-Gruppe Symmetriebrechung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007164431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT fieldmichael symmetrybreakingforcompactliegroups |