Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
Dynamics and symmetry [[electronic resource] /] / Michael J. Field
| Dynamics and symmetry [[electronic resource] /] / Michael J. Field |
| Autore | Field Mike |
| Pubbl/distr/stampa | London, : Imperial College Press |
| Descrizione fisica | 1 online resource (492 p.) |
| Disciplina | 515.35 |
| Collana | ICP advanced texts in mathematics |
| Soggetto topico |
Topological dynamics
Lie groups Hamiltonian systems Bifurcation theory Symmetry (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-86756-X
9786611867560 1-86094-854-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 1. Groups; 1.1 Definition of a group and examples; 1.2 Homomorphisms, subgroups and quotient groups; 1.2.1 Generators and relations for .nite groups; 1.3 Constructions; 1.4 Topological groups; 1.5 Lie groups; 1.5.1 The Lie bracket of vector fields; 1.5.2 The Lie algebra of G; 1.5.3 The exponential map of g; 1.5.4 Additional properties of brackets and exp; 1.5.5 Closed subgroups of a Lie group; 1.6 Haarmeasure; 2. Group Actions and Representations; 2.1 Introduction; 2.2 Groups and G-spaces; 2.2.1 Continuous actions and G-spaces; 2.3 Orbit spaces and actions
2.4 Twisted products2.4.1 Induced G-spaces; 2.5 Isotropy type and stratification by isotropy type; 2.6 Representations; 2.6.1 Averaging over G; 2.7 Irreducible representations and the isotypic decomposition; 2.7.1 C-representations; 2.7.2 Absolutely irreducible representations; 2.8 Orbit structure for representations; 2.9 Slices; 2.9.1 Slices for linear finite group actions; 2.10 Invariant and equivariant maps; 2.10.1 Smooth invariant and equivariant maps on representations; 2.10.2 Equivariant vector fields and flows; 3. Smooth G-manifolds; 3.1 Proper G-manifolds; 3.1.1 Proper free actions 3.2 G-vector bundles3.3 Infinitesimal theory; 3.4 Riemannianmanifolds; 3.4.1 Exponential map of a complete Riemannian manifold; 3.4.2 The tubular neighbourhood theorem; 3.4.3 Riemannian G-manifolds; 3.5 The differentiable slice theorem; 3.6 Equivariant isotopy extension theorem; 3.7 Orbit structure for G-manifolds; 3.7.1 Closed filtration of M by isotropy type; 3.8 The stratification of M by normal isotropy type; 3.9 Stratified sets; 3.9.1 Transversality to a Whitney stratification; 3.9.2 Regularity of stratification by normal isotropy type 3.10 Invariant Riemannian metrics on a compact Lie group3.10.1 The adjoint representations; 3.10.2 The exponential map; 3.10.3 Closed subgroups of a Lie group; 4. Equivariant Bifurcation Theory: Steady State Bifurcation; 4.1 Introduction and preliminaries; 4.1.1 Normalized families; 4.2 Solution branches and the branching pattern; 4.2.1 Stability of branching patterns; 4.3 Symmetry breaking-theMISC; 4.3.1 Symmetry breaking isotropy types; 4.3.2 Maximal isotropy subgroup conjecture; 4.4 Determinacy; 4.4.1 Polynomial maps; 4.4.2 Finite determinacy; 4.5 The hyperoctahedral family 4.5.1 The representations (Rk,Hk)4.5.2 Invariants and equivariants for Hk; 4.5.3 Cubic equivariants for Hk; 4.5.4 Bifurcation for cubic families; 4.5.5 Subgroups of Hk; 4.5.6 Some subgroups of the symmetric group; 4.5.7 A big family of counterexamples to the MISC; 4.5.8 Examples where P3G (Rk, Rk) = P3H k (Rk, Rk); 4.5.9 Stable solution branches of maximal index and trivial isotropy; 4.5.10 An example with applications to phase transitions; 4.6 Phase vector field and maps of hyperbolic type; 4.6.1 Cubic polynomial maps; 4.6.2 Phase vector field; 4.6.3 Normalized families 4.6.4 Maps of hyperbolic type |
| Record Nr. | UNINA-9910458099103321 |
Field Mike
|
||
| London, : Imperial College Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Dynamics and symmetry [[electronic resource] /] / Michael J. Field
| Dynamics and symmetry [[electronic resource] /] / Michael J. Field |
| Autore | Field Mike |
| Pubbl/distr/stampa | London, : Imperial College Press |
| Descrizione fisica | 1 online resource (492 p.) |
| Disciplina | 515.35 |
| Collana | ICP advanced texts in mathematics |
| Soggetto topico |
Topological dynamics
Lie groups Hamiltonian systems Bifurcation theory Symmetry (Mathematics) |
| ISBN |
1-281-86756-X
9786611867560 1-86094-854-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 1. Groups; 1.1 Definition of a group and examples; 1.2 Homomorphisms, subgroups and quotient groups; 1.2.1 Generators and relations for .nite groups; 1.3 Constructions; 1.4 Topological groups; 1.5 Lie groups; 1.5.1 The Lie bracket of vector fields; 1.5.2 The Lie algebra of G; 1.5.3 The exponential map of g; 1.5.4 Additional properties of brackets and exp; 1.5.5 Closed subgroups of a Lie group; 1.6 Haarmeasure; 2. Group Actions and Representations; 2.1 Introduction; 2.2 Groups and G-spaces; 2.2.1 Continuous actions and G-spaces; 2.3 Orbit spaces and actions
2.4 Twisted products2.4.1 Induced G-spaces; 2.5 Isotropy type and stratification by isotropy type; 2.6 Representations; 2.6.1 Averaging over G; 2.7 Irreducible representations and the isotypic decomposition; 2.7.1 C-representations; 2.7.2 Absolutely irreducible representations; 2.8 Orbit structure for representations; 2.9 Slices; 2.9.1 Slices for linear finite group actions; 2.10 Invariant and equivariant maps; 2.10.1 Smooth invariant and equivariant maps on representations; 2.10.2 Equivariant vector fields and flows; 3. Smooth G-manifolds; 3.1 Proper G-manifolds; 3.1.1 Proper free actions 3.2 G-vector bundles3.3 Infinitesimal theory; 3.4 Riemannianmanifolds; 3.4.1 Exponential map of a complete Riemannian manifold; 3.4.2 The tubular neighbourhood theorem; 3.4.3 Riemannian G-manifolds; 3.5 The differentiable slice theorem; 3.6 Equivariant isotopy extension theorem; 3.7 Orbit structure for G-manifolds; 3.7.1 Closed filtration of M by isotropy type; 3.8 The stratification of M by normal isotropy type; 3.9 Stratified sets; 3.9.1 Transversality to a Whitney stratification; 3.9.2 Regularity of stratification by normal isotropy type 3.10 Invariant Riemannian metrics on a compact Lie group3.10.1 The adjoint representations; 3.10.2 The exponential map; 3.10.3 Closed subgroups of a Lie group; 4. Equivariant Bifurcation Theory: Steady State Bifurcation; 4.1 Introduction and preliminaries; 4.1.1 Normalized families; 4.2 Solution branches and the branching pattern; 4.2.1 Stability of branching patterns; 4.3 Symmetry breaking-theMISC; 4.3.1 Symmetry breaking isotropy types; 4.3.2 Maximal isotropy subgroup conjecture; 4.4 Determinacy; 4.4.1 Polynomial maps; 4.4.2 Finite determinacy; 4.5 The hyperoctahedral family 4.5.1 The representations (Rk,Hk)4.5.2 Invariants and equivariants for Hk; 4.5.3 Cubic equivariants for Hk; 4.5.4 Bifurcation for cubic families; 4.5.5 Subgroups of Hk; 4.5.6 Some subgroups of the symmetric group; 4.5.7 A big family of counterexamples to the MISC; 4.5.8 Examples where P3G (Rk, Rk) = P3H k (Rk, Rk); 4.5.9 Stable solution branches of maximal index and trivial isotropy; 4.5.10 An example with applications to phase transitions; 4.6 Phase vector field and maps of hyperbolic type; 4.6.1 Cubic polynomial maps; 4.6.2 Phase vector field; 4.6.3 Normalized families 4.6.4 Maps of hyperbolic type |
| Record Nr. | UNINA-9910784890203321 |
|
Field Mike
|
||
| London, : Imperial College Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Dynamics and symmetry / / Michael J. Field
| Dynamics and symmetry / / Michael J. Field |
| Autore | Field Mike |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | London, : Imperial College Press |
| Descrizione fisica | 1 online resource (492 p.) |
| Disciplina | 515.35 |
| Collana | ICP advanced texts in mathematics |
| Soggetto topico |
Topological dynamics
Lie groups Hamiltonian systems Bifurcation theory Symmetry (Mathematics) |
| ISBN |
1-281-86756-X
9786611867560 1-86094-854-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 1. Groups; 1.1 Definition of a group and examples; 1.2 Homomorphisms, subgroups and quotient groups; 1.2.1 Generators and relations for .nite groups; 1.3 Constructions; 1.4 Topological groups; 1.5 Lie groups; 1.5.1 The Lie bracket of vector fields; 1.5.2 The Lie algebra of G; 1.5.3 The exponential map of g; 1.5.4 Additional properties of brackets and exp; 1.5.5 Closed subgroups of a Lie group; 1.6 Haarmeasure; 2. Group Actions and Representations; 2.1 Introduction; 2.2 Groups and G-spaces; 2.2.1 Continuous actions and G-spaces; 2.3 Orbit spaces and actions
2.4 Twisted products2.4.1 Induced G-spaces; 2.5 Isotropy type and stratification by isotropy type; 2.6 Representations; 2.6.1 Averaging over G; 2.7 Irreducible representations and the isotypic decomposition; 2.7.1 C-representations; 2.7.2 Absolutely irreducible representations; 2.8 Orbit structure for representations; 2.9 Slices; 2.9.1 Slices for linear finite group actions; 2.10 Invariant and equivariant maps; 2.10.1 Smooth invariant and equivariant maps on representations; 2.10.2 Equivariant vector fields and flows; 3. Smooth G-manifolds; 3.1 Proper G-manifolds; 3.1.1 Proper free actions 3.2 G-vector bundles3.3 Infinitesimal theory; 3.4 Riemannianmanifolds; 3.4.1 Exponential map of a complete Riemannian manifold; 3.4.2 The tubular neighbourhood theorem; 3.4.3 Riemannian G-manifolds; 3.5 The differentiable slice theorem; 3.6 Equivariant isotopy extension theorem; 3.7 Orbit structure for G-manifolds; 3.7.1 Closed filtration of M by isotropy type; 3.8 The stratification of M by normal isotropy type; 3.9 Stratified sets; 3.9.1 Transversality to a Whitney stratification; 3.9.2 Regularity of stratification by normal isotropy type 3.10 Invariant Riemannian metrics on a compact Lie group3.10.1 The adjoint representations; 3.10.2 The exponential map; 3.10.3 Closed subgroups of a Lie group; 4. Equivariant Bifurcation Theory: Steady State Bifurcation; 4.1 Introduction and preliminaries; 4.1.1 Normalized families; 4.2 Solution branches and the branching pattern; 4.2.1 Stability of branching patterns; 4.3 Symmetry breaking-theMISC; 4.3.1 Symmetry breaking isotropy types; 4.3.2 Maximal isotropy subgroup conjecture; 4.4 Determinacy; 4.4.1 Polynomial maps; 4.4.2 Finite determinacy; 4.5 The hyperoctahedral family 4.5.1 The representations (Rk,Hk)4.5.2 Invariants and equivariants for Hk; 4.5.3 Cubic equivariants for Hk; 4.5.4 Bifurcation for cubic families; 4.5.5 Subgroups of Hk; 4.5.6 Some subgroups of the symmetric group; 4.5.7 A big family of counterexamples to the MISC; 4.5.8 Examples where P3G (Rk, Rk) = P3H k (Rk, Rk); 4.5.9 Stable solution branches of maximal index and trivial isotropy; 4.5.10 An example with applications to phase transitions; 4.6 Phase vector field and maps of hyperbolic type; 4.6.1 Cubic polynomial maps; 4.6.2 Phase vector field; 4.6.3 Normalized families 4.6.4 Maps of hyperbolic type |
| Record Nr. | UNINA-9910813168403321 |
|
Field Mike
|
||
| London, : Imperial College Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Ergodic theory of equivariant diffeomorphisms : Markov partitions and stable ergodicity / / Michael Field, Matthew Nicol
| Ergodic theory of equivariant diffeomorphisms : Markov partitions and stable ergodicity / / Michael Field, Matthew Nicol |
| Autore | Field Mike |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (113 p.) |
| Disciplina | 515.48 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Ergodic theory
Diffeomorphisms |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0401-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Equivariant Geometry and Dynamics""; ""2.1. Lie groups, Î?-manifolds and representations""; ""2.1.1. Compact Lie groups""; ""2.1.2. Î?-manifolds""; ""2.2. Equivariant dynamical systems""; ""2.2.1. Discrete dynamical systems""; ""2.2.2. Skew and principal extensions""; ""2.2.3. Continuous dynamical systems""; ""2.3. Local theory""; ""2.4. Invariant subspaces and transversality""; ""2.5. Basic sets for equivariant diffeomorphisms""; ""Chapter 3. Technical preliminaries""; ""3.1. Geometry of group actions and maps""
""4.4. Existence of Î?-regular Markov partitions""""Chapter 5. Transversally hyperbolic sets""; ""5.1. Transverse hyperbolicity""; ""5.2. Properties of transversally hyperbolic sets""; ""5.3. Î?-expansiveness""; ""5.4. Stability properties of transversally hyperbolic sets""; ""5.5. Subshifts of finite type and attractors""; ""5.6. Local product structure""; ""5.7. Expansiveness and shadowing""; ""5.8. Stability of basic sets""; ""Chapter 6. Markov partitions for basic sets""; ""6.1. Rectangles""; ""6.2. Slices""; ""6.3. Pre-Markov partitions""; ""6.4. Proper and admissible rectangles"" ""6.5. Î?-regular Markov partitions""""6.6. Construction of Î?-regular Markov partitions""; ""Part 2. Stable Ergodicity""; ""Chapter 7. Preliminaries""; ""7.1. Metrics""; ""7.2. The Haar lift""; ""7.3. Isotropy and ergodicity""; ""7.4. Î?-regular Markov partitions""; ""7.5. Measures on the orbit space""; ""7.6. Spectral characterization of ergodicity and weak-mixing""; ""Chapter 8. LivÅ¡ic regularity and ergodic components""; ""8.1. LivÅ¡ic regularity""; ""8.2. Structure of ergodic components""; ""Chapter 9. Stable Ergodicity""; ""9.1. Stable ergodicity: Î? compact and connected"" ""9.2. Stable ergodicity: Î? semisimple""""9.3. Stable ergodicity for attractors""; ""9.4. Stable ergodicity and SRB attractors""; ""Appendix A. On the absolute continuity of v""; ""Bibliography"" |
| Record Nr. | UNINA-9910480873103321 |
|
Field Mike
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Ergodic theory of equivariant diffeomorphisms : Markov partitions and stable ergodicity / / Michael Field, Matthew Nicol
| Ergodic theory of equivariant diffeomorphisms : Markov partitions and stable ergodicity / / Michael Field, Matthew Nicol |
| Autore | Field Mike |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (113 p.) |
| Disciplina | 515.48 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Ergodic theory
Diffeomorphisms |
| ISBN | 1-4704-0401-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Equivariant Geometry and Dynamics""; ""2.1. Lie groups, Î?-manifolds and representations""; ""2.1.1. Compact Lie groups""; ""2.1.2. Î?-manifolds""; ""2.2. Equivariant dynamical systems""; ""2.2.1. Discrete dynamical systems""; ""2.2.2. Skew and principal extensions""; ""2.2.3. Continuous dynamical systems""; ""2.3. Local theory""; ""2.4. Invariant subspaces and transversality""; ""2.5. Basic sets for equivariant diffeomorphisms""; ""Chapter 3. Technical preliminaries""; ""3.1. Geometry of group actions and maps""
""4.4. Existence of Î?-regular Markov partitions""""Chapter 5. Transversally hyperbolic sets""; ""5.1. Transverse hyperbolicity""; ""5.2. Properties of transversally hyperbolic sets""; ""5.3. Î?-expansiveness""; ""5.4. Stability properties of transversally hyperbolic sets""; ""5.5. Subshifts of finite type and attractors""; ""5.6. Local product structure""; ""5.7. Expansiveness and shadowing""; ""5.8. Stability of basic sets""; ""Chapter 6. Markov partitions for basic sets""; ""6.1. Rectangles""; ""6.2. Slices""; ""6.3. Pre-Markov partitions""; ""6.4. Proper and admissible rectangles"" ""6.5. Î?-regular Markov partitions""""6.6. Construction of Î?-regular Markov partitions""; ""Part 2. Stable Ergodicity""; ""Chapter 7. Preliminaries""; ""7.1. Metrics""; ""7.2. The Haar lift""; ""7.3. Isotropy and ergodicity""; ""7.4. Î?-regular Markov partitions""; ""7.5. Measures on the orbit space""; ""7.6. Spectral characterization of ergodicity and weak-mixing""; ""Chapter 8. LivÅ¡ic regularity and ergodic components""; ""8.1. LivÅ¡ic regularity""; ""8.2. Structure of ergodic components""; ""Chapter 9. Stable Ergodicity""; ""9.1. Stable ergodicity: Î? compact and connected"" ""9.2. Stable ergodicity: Î? semisimple""""9.3. Stable ergodicity for attractors""; ""9.4. Stable ergodicity and SRB attractors""; ""Appendix A. On the absolute continuity of v""; ""Bibliography"" |
| Record Nr. | UNINA-9910788746603321 |
|
Field Mike
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Ergodic theory of equivariant diffeomorphisms : Markov partitions and stable ergodicity / / Michael Field, Matthew Nicol
| Ergodic theory of equivariant diffeomorphisms : Markov partitions and stable ergodicity / / Michael Field, Matthew Nicol |
| Autore | Field Mike |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (113 p.) |
| Disciplina | 515.48 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Ergodic theory
Diffeomorphisms |
| ISBN | 1-4704-0401-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Equivariant Geometry and Dynamics""; ""2.1. Lie groups, Î?-manifolds and representations""; ""2.1.1. Compact Lie groups""; ""2.1.2. Î?-manifolds""; ""2.2. Equivariant dynamical systems""; ""2.2.1. Discrete dynamical systems""; ""2.2.2. Skew and principal extensions""; ""2.2.3. Continuous dynamical systems""; ""2.3. Local theory""; ""2.4. Invariant subspaces and transversality""; ""2.5. Basic sets for equivariant diffeomorphisms""; ""Chapter 3. Technical preliminaries""; ""3.1. Geometry of group actions and maps""
""4.4. Existence of Î?-regular Markov partitions""""Chapter 5. Transversally hyperbolic sets""; ""5.1. Transverse hyperbolicity""; ""5.2. Properties of transversally hyperbolic sets""; ""5.3. Î?-expansiveness""; ""5.4. Stability properties of transversally hyperbolic sets""; ""5.5. Subshifts of finite type and attractors""; ""5.6. Local product structure""; ""5.7. Expansiveness and shadowing""; ""5.8. Stability of basic sets""; ""Chapter 6. Markov partitions for basic sets""; ""6.1. Rectangles""; ""6.2. Slices""; ""6.3. Pre-Markov partitions""; ""6.4. Proper and admissible rectangles"" ""6.5. Î?-regular Markov partitions""""6.6. Construction of Î?-regular Markov partitions""; ""Part 2. Stable Ergodicity""; ""Chapter 7. Preliminaries""; ""7.1. Metrics""; ""7.2. The Haar lift""; ""7.3. Isotropy and ergodicity""; ""7.4. Î?-regular Markov partitions""; ""7.5. Measures on the orbit space""; ""7.6. Spectral characterization of ergodicity and weak-mixing""; ""Chapter 8. LivÅ¡ic regularity and ergodic components""; ""8.1. LivÅ¡ic regularity""; ""8.2. Structure of ergodic components""; ""Chapter 9. Stable Ergodicity""; ""9.1. Stable ergodicity: Î? compact and connected"" ""9.2. Stable ergodicity: Î? semisimple""""9.3. Stable ergodicity for attractors""; ""9.4. Stable ergodicity and SRB attractors""; ""Appendix A. On the absolute continuity of v""; ""Bibliography"" |
| Record Nr. | UNINA-9910820408503321 |
|
Field Mike
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Symmetry breaking for compact Lie groups / / Michael Field
| Symmetry breaking for compact Lie groups / / Michael Field |
| Autore | Field Mike |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1996 |
| Descrizione fisica | 1 online resource (185 p.) |
| Disciplina | 515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Bifurcation theory
Lie groups |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0159-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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- 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"" |
| Record Nr. | UNINA-9910480196103321 |
|
Field Mike
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Symmetry breaking for compact Lie groups / / Michael Field
| Symmetry breaking for compact Lie groups / / Michael Field |
| Autore | Field Mike |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1996 |
| Descrizione fisica | 1 online resource (185 p.) |
| Disciplina | 515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Bifurcation theory
Lie groups |
| ISBN | 1-4704-0159-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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- 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"" |
| Record Nr. | UNINA-9910788759303321 |
|
Field Mike
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Symmetry breaking for compact Lie groups / / Michael Field
| Symmetry breaking for compact Lie groups / / Michael Field |
| Autore | Field Mike |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1996 |
| Descrizione fisica | 1 online resource (185 p.) |
| Disciplina | 515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Bifurcation theory
Lie groups |
| ISBN | 1-4704-0159-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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- 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"" |
| Record Nr. | UNINA-9910827875003321 |
|
Field Mike
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||