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Singularity theory for non-twist KAM tori / / A. González-Enríquez, A. Haro, R. de la Llave
| Singularity theory for non-twist KAM tori / / A. González-Enríquez, A. Haro, R. de la Llave |
| Autore | González-Enríquez A (Alejandra), <1967-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (128 p.) |
| Disciplina | 515.39 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Bifurcation theory
Perturbation (Mathematics) Ergodic theory |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-1428-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Part 1 . Introduction and preliminaries""; ""Chapter 1. Introduction""; ""1.1. Towards a singularity theory for KAM tori""; ""1.2. Methodology (a brief description)""; ""1.3. Outline of this monograph""; ""Chapter 2. Preliminaries""; ""2.1. Elementary notations""; ""2.2. Geometric preliminaries""; ""2.3. Symplectic deformations and moment maps""; ""2.4. Analytic preliminaries""; ""2.5. Cohomology equations""; ""Part 2 . Geometrical properties of KAM invariant tori""; ""Chapter 3. Geometric properties of an invariant torus""; ""3.1. Automatic reducibility""
""3.2. Geometric definition of non-twist tori""""3.3. Intrinsic character of the reducibility and of the torsion""; ""Chapter 4. Geometric properties of fibered Lagrangian deformations""; ""4.1. The potential of a fibered Lagrangian deformation""; ""4.2. A parametric version of the potential""; ""Part 3 . KAM results""; ""Chapter 5. Nondegeneracy on a KAM procedure with fixed frequency""; ""5.1. Approximate reducibility of approximately invariant tori""; ""5.2. Dummy and modifying parameters""; ""Chapter 6. A KAM theorem for symplectic deformations"" ""6.1. Functional equations and nondegeneracy condition""""6.2. Statement of the KAM theorem""; ""6.3. Proof of the KAM Theorem""; ""Chapter 7. A Transformed Tori Theorem""; ""7.1. Nondegeneracy condition""; ""7.2. Statement of the Transformed Tori Theorem""; ""7.3. Proof of the Transformed Tori Theorem""; ""Part 4 . Singularity theory for KAM tori""; ""Chapter 8. Bifurcation theory for KAM tori""; ""8.1. Classification of KAM invariant tori""; ""8.2. Local equivalence of Bifurcations diagrams""; ""Chapter 9. The close-to-integrable case""; ""9.1. The integrable case"" ""9.2. Persistence of invariant tori in quasi-integrable systems""""9.3. Unfolding non-twist tori""; ""9.4. The Birkhoff potential and the potential of an invariant torus""; ""Appendices""; ""Appendix A. Hamiltonian vector fields""; ""A.1. Cohomology equations""; ""A.2. Automatic reducibility of invariant tori""; ""A.3. Families of Hamiltonians and moment maps""; ""A.4. Potential and moment of an invariant FLD""; ""A.5. Transformed Tori Theorem""; ""A.6. A KAM Theorem for families of Hamiltonians""; ""Appendix B. Elements of singularity theory""; ""Bibliography"" |
| Record Nr. | UNINA-9910480615103321 |
González-Enríquez A (Alejandra), <1967->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Singularity theory for non-twist KAM tori / / A. González-Enríquez, A. Haro, R. de la Llave
| Singularity theory for non-twist KAM tori / / A. González-Enríquez, A. Haro, R. de la Llave |
| Autore | González-Enríquez A (Alejandra), <1967-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (128 p.) |
| Disciplina | 515.39 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Bifurcation theory
Perturbation (Mathematics) Ergodic theory |
| ISBN | 1-4704-1428-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Part 1 . Introduction and preliminaries""; ""Chapter 1. Introduction""; ""1.1. Towards a singularity theory for KAM tori""; ""1.2. Methodology (a brief description)""; ""1.3. Outline of this monograph""; ""Chapter 2. Preliminaries""; ""2.1. Elementary notations""; ""2.2. Geometric preliminaries""; ""2.3. Symplectic deformations and moment maps""; ""2.4. Analytic preliminaries""; ""2.5. Cohomology equations""; ""Part 2 . Geometrical properties of KAM invariant tori""; ""Chapter 3. Geometric properties of an invariant torus""; ""3.1. Automatic reducibility""
""3.2. Geometric definition of non-twist tori""""3.3. Intrinsic character of the reducibility and of the torsion""; ""Chapter 4. Geometric properties of fibered Lagrangian deformations""; ""4.1. The potential of a fibered Lagrangian deformation""; ""4.2. A parametric version of the potential""; ""Part 3 . KAM results""; ""Chapter 5. Nondegeneracy on a KAM procedure with fixed frequency""; ""5.1. Approximate reducibility of approximately invariant tori""; ""5.2. Dummy and modifying parameters""; ""Chapter 6. A KAM theorem for symplectic deformations"" ""6.1. Functional equations and nondegeneracy condition""""6.2. Statement of the KAM theorem""; ""6.3. Proof of the KAM Theorem""; ""Chapter 7. A Transformed Tori Theorem""; ""7.1. Nondegeneracy condition""; ""7.2. Statement of the Transformed Tori Theorem""; ""7.3. Proof of the Transformed Tori Theorem""; ""Part 4 . Singularity theory for KAM tori""; ""Chapter 8. Bifurcation theory for KAM tori""; ""8.1. Classification of KAM invariant tori""; ""8.2. Local equivalence of Bifurcations diagrams""; ""Chapter 9. The close-to-integrable case""; ""9.1. The integrable case"" ""9.2. Persistence of invariant tori in quasi-integrable systems""""9.3. Unfolding non-twist tori""; ""9.4. The Birkhoff potential and the potential of an invariant torus""; ""Appendices""; ""Appendix A. Hamiltonian vector fields""; ""A.1. Cohomology equations""; ""A.2. Automatic reducibility of invariant tori""; ""A.3. Families of Hamiltonians and moment maps""; ""A.4. Potential and moment of an invariant FLD""; ""A.5. Transformed Tori Theorem""; ""A.6. A KAM Theorem for families of Hamiltonians""; ""Appendix B. Elements of singularity theory""; ""Bibliography"" |
| Record Nr. | UNINA-9910796031603321 |
|
González-Enríquez A (Alejandra), <1967->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Singularity theory for non-twist KAM tori / / A. González-Enríquez, A. Haro, R. de la Llave
| Singularity theory for non-twist KAM tori / / A. González-Enríquez, A. Haro, R. de la Llave |
| Autore | González-Enríquez A (Alejandra), <1967-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (128 p.) |
| Disciplina | 515.39 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Bifurcation theory
Perturbation (Mathematics) Ergodic theory |
| ISBN | 1-4704-1428-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Part 1 . Introduction and preliminaries""; ""Chapter 1. Introduction""; ""1.1. Towards a singularity theory for KAM tori""; ""1.2. Methodology (a brief description)""; ""1.3. Outline of this monograph""; ""Chapter 2. Preliminaries""; ""2.1. Elementary notations""; ""2.2. Geometric preliminaries""; ""2.3. Symplectic deformations and moment maps""; ""2.4. Analytic preliminaries""; ""2.5. Cohomology equations""; ""Part 2 . Geometrical properties of KAM invariant tori""; ""Chapter 3. Geometric properties of an invariant torus""; ""3.1. Automatic reducibility""
""3.2. Geometric definition of non-twist tori""""3.3. Intrinsic character of the reducibility and of the torsion""; ""Chapter 4. Geometric properties of fibered Lagrangian deformations""; ""4.1. The potential of a fibered Lagrangian deformation""; ""4.2. A parametric version of the potential""; ""Part 3 . KAM results""; ""Chapter 5. Nondegeneracy on a KAM procedure with fixed frequency""; ""5.1. Approximate reducibility of approximately invariant tori""; ""5.2. Dummy and modifying parameters""; ""Chapter 6. A KAM theorem for symplectic deformations"" ""6.1. Functional equations and nondegeneracy condition""""6.2. Statement of the KAM theorem""; ""6.3. Proof of the KAM Theorem""; ""Chapter 7. A Transformed Tori Theorem""; ""7.1. Nondegeneracy condition""; ""7.2. Statement of the Transformed Tori Theorem""; ""7.3. Proof of the Transformed Tori Theorem""; ""Part 4 . Singularity theory for KAM tori""; ""Chapter 8. Bifurcation theory for KAM tori""; ""8.1. Classification of KAM invariant tori""; ""8.2. Local equivalence of Bifurcations diagrams""; ""Chapter 9. The close-to-integrable case""; ""9.1. The integrable case"" ""9.2. Persistence of invariant tori in quasi-integrable systems""""9.3. Unfolding non-twist tori""; ""9.4. The Birkhoff potential and the potential of an invariant torus""; ""Appendices""; ""Appendix A. Hamiltonian vector fields""; ""A.1. Cohomology equations""; ""A.2. Automatic reducibility of invariant tori""; ""A.3. Families of Hamiltonians and moment maps""; ""A.4. Potential and moment of an invariant FLD""; ""A.5. Transformed Tori Theorem""; ""A.6. A KAM Theorem for families of Hamiltonians""; ""Appendix B. Elements of singularity theory""; ""Bibliography"" |
| Record Nr. | UNINA-9910828119103321 |
|
González-Enríquez A (Alejandra), <1967->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||