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Record Nr. |
UNINA9910827875003321 |
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Autore |
Field Mike |
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Titolo |
Symmetry breaking for compact Lie groups / / Michael Field |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 1996 |
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©1996 |
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ISBN |
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Descrizione fisica |
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1 online resource (185 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; Number 574 |
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Disciplina |
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Soggetti |
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Bifurcation theory |
Lie groups |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"March 1996, Volume 120, Number 574 (second of 4 numbers)." |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""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. |
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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- up""""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""; ""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"" |
""9.13. Symmetric structure of parametrizations"" |
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