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Symmetry breaking for compact Lie groups /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
1996.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 574. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- ""Contents""; ""1. Introduction""; ""1.1. Notes for the reader""; ""1.2. Acknowledgements""; ""2. Technical Preliminaries and Basic Notations""; ""2.1. Î?-sets and isotropy types""; ""2.2. Representations""; ""2.3. Isotropy types for representations""; ""2.4. Polynomial Invariants and Equivariants""; ""2.5. Smooth families of equivariant maps""; ""2.6. Normalized families""; ""3. Branching and invariant group orbits""; ""3.1. Relative equilibria and normal hyperbolicity""; ""3.2. Branches of relative equilibria""; ""3.3. The branching pattern""; ""3.4. Stabilities""
- ""3.5. Branching conditions""""3.6. The signed indexed branching pattern""; ""3.7. Stable families""; ""3.8. Determinacy""; ""3.9. Strong determinacy""; ""4. Genericity theorems""; ""4.1. Semi-algebraic and semi-analytic sets""; ""4.2. Invariant and equi variant generators""; ""4.3. The variety Σ""; ""4.4. Stability theorems I: Weak regularity""; ""4.5. Stability theorems II: Regular families""; ""4.6. Determinacy""; ""4.7. Examples related to finite reflection groups""; ""5. Finitely determined bifurcation problems I""; ""5.1. The phase vector field""
- ""5.2. The spaces A[sub(h)](Î?,V), B[sub(h)](Î?,V)""""5.3. Strong determinacy""; ""6. Finitely-determined bifurcation problems II""; ""6.1. Statement of the main theorem""; ""6.2. 2-stable relative equilibria""; ""7. Strong determinacy: Technical preliminaries""; ""7.1. Introduction""; ""7.2. Notational conventions""; ""7.3. Local geometry""; ""7.4. Weakly regular families""; ""7.5. Analytic families and solution branches""; ""7.6. Compatible parametrizations and initial exponents""; ""7.7. Remarks on the set Î?(f)""; ""7.8. The parametrization theorem""; ""7.9. The space R[sup(2)]""
- ""7.10. Initial exponents and the space R[sup(3)]""""8. Strong determinacy: Î? finite""; ""8.1. Analytic parametrizations""; ""8.2. Estimates on eigenvalues""; ""8.3. Fractional power series""; ""8.4. Eigenvalue estimates: Analytic case""; ""8.5. Eigenvalue estimates: Smooth case""; ""8.6. Proof of Theorem 8.2.6""; ""8.7. Strong determinacy: Î? finite""; ""8.8. Formation of new branches under perturbation""; ""9. Strong determinacy: Î? compact, non-finite""; ""9.1. Polar blowing-up: Local theory""; ""9.2. Polar blowing-up: Global theory""; ""9.3. Polar blowing-up a Î?-manifold""
- 9.4. Blowing- up9.4.1. Blowing-up along a linear subspace
- 9.4.2. Blowing-up analytic varieties
- 9.4.3. Blowing-up algebraic varieties
- 9.5. Conical sets
- 9.6. Algebraic and analytic structure of the orbit strata
- 9.7. Blowing-up representations
- 9.7.1. Analytic theory
- 9.7.2. Algebraic theory
- 9.8. A tangent and normal decomposition
- 9.9. Blowing-up arcs
- 9.10. Analytic parametrizations of solution branches
- 9.11. Lifting analytic parametrizations
- 9.12. Controlling the lifts of analytic parametrizations