On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems / / P. Lochak, J.-P. Marco, D. Sauzin
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| Autore: |
Lochak P (Pierre)
|
| Titolo: |
On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems / / P. Lochak, J.-P. Marco, D. Sauzin
|
| Pubblicazione: | Providence, Rhode Island : , : American Mathematical Society, , 2003 |
| Descrizione fisica: | 1 online resource (162 p.) |
| Disciplina: | 510 s |
| 514/.74 | |
| Soggetto topico: | Hamiltonian systems |
| Invariant manifolds | |
| Persona (resp. second.): | MarcoJ.-P |
| SauzinD. <1966-> | |
| Note generali: | "Volume 163, number 775 (second of 5 numbers)." |
| Nota di bibliografia: | Includes bibliographical references. |
| Nota di contenuto: | ""Contents""; ""Chapter 0. Introduction and Some Salient Features of the Model Hamiltonian""; ""Chapter 1. Symplectic Geometry and the Splitting of Invariant Manifolds""; ""Â 1.1. Symplectic geometry: a short reminder""; ""Â 1.2. Hyperbolic invariant manifolds""; ""Â 1.3. Angles of Lagrangian planes: the symplectic viewpoint""; ""Â 1.4. Angles of Lagrangian planes: the Euclidean viewpoint""; ""Â 1.5. Symplectic isomorphisms, angles and splitting forms""; ""Â 1.6. The splitting of Lagrangian submanifolds""; ""Â 1.7. Lagrangian submanifolds in a cotangent bundle"" |
| ""Â 1.8. Hyperbolic tori and normally hyperbolic invariant manifolds""""Â 1.9. The perturbative setting""; ""Â 1.10. Lagrangian intersections and homoclinic trajectories""; ""Â 1.11. The splitting of the invariant manifolds of hyperbolic tori""; ""Chapter 2. Estimating the Splitting Matrix Using Normal Forms""; ""Â 2.1. Resonant normal forms""; ""Â 2.2. Computations in the vicinity of a resonant surface""; ""Â 2.3. Splitting in a perturbative setting, variance and stability""; ""Â 2.4. General exponential estimates for the splitting matrix"" | |
| "" 2.5. Persistence of tori, invariant manifolds and homoclinic trajectories"""" 2.6. Splitting and stability""; ""Chapter 3. The Hamilton�Jacobi Method for a Simple Resonance""; "" 3.1. Notation and assumptions""; "" 3.2. Formal solutions and the Hamilton�Jacobi algorithm""; "" 3.3. Convergence and domains of analyticity""; "" 3.4. Exponential closeness of the invariant manifolds""; "" 3.5. Linear versus nonlinear splitting""; "" 3.6. Some variants and possible generalizations""; "" 3.7. A short historical tour and some concluding remarks"" | |
| ""Appendix. Invariant Tori With Vanishing or Zero Torsion""""Bibliography "" | |
| Titolo autorizzato: | On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems |
| ISBN: | 1-4704-0373-0 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910813657203321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Memoirs of the American Mathematical Society ; ; no. 775.