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Autore: | González-Enríquez A (Alejandra), <1967-> |
Titolo: | Singularity theory for non-twist KAM tori / / A. González-Enríquez, A. Haro, R. de la Llave |
Pubblicazione: | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
©2013 | |
Descrizione fisica: | 1 online resource (128 p.) |
Disciplina: | 515.39 |
Soggetto topico: | Bifurcation theory |
Perturbation (Mathematics) | |
Ergodic theory | |
Persona (resp. second.): | HaroA <1969-> (Alex) |
De la LlaveRafael <1957-> | |
Note generali: | "Volume 227, Number 1067 (third of 4 numbers)." |
Nota di bibliografia: | Includes bibliographical references. |
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"" | |
Titolo autorizzato: | Singularity theory for non-twist KAM tori |
ISBN: | 1-4704-1428-7 |
Formato: | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910796031603321 |
Lo trovi qui: | Univ. Federico II |
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