On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems / / P. Lochak, J.-P. Marco, D. Sauzin

• Record Nr.: UNINA9910788849003321
• Autore: Lochak P (Pierre)
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2003
• ISBN: 1-4704-0373-0
• Descrizione fisica: 1 online resource (162 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 775
• Disciplina: 510 s; 514/.74
• Soggetti: Hamiltonian systems; Invariant manifolds
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• 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""; "" 1.1. Symplectic geometry: a short reminder""; "" 1.2. Hyperbolic invariant manifolds""; "" 1.3. Angles of Lagrangian planes: the symplectic viewpoint""; "" 1.4. Angles of Lagrangian planes: the Euclidean viewpoint""; "" 1.5. Symplectic isomorphisms, angles and splitting forms""; "" 1.6. The splitting of Lagrangian submanifolds""; "" 1.7. Lagrangian submanifolds in a cotangent bundle""; "" 1.8. Hyperbolic tori and normally hyperbolic invariant manifolds"""" 1.9. The perturbative setting""; "" 1.10. Lagrangian intersections and homoclinic trajectories""; "" 1.11. The splitting of the invariant manifolds of hyperbolic tori""; ""Chapter 2. Estimating the Splitting Matrix Using Normal Forms""; "" 2.1. Resonant normal forms""; "" 2.2. Computations in the vicinity of a resonant surface""; "" 2.3. Splitting in a perturbative setting, variance and stability""; "" 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 Hamiltonâ€?Jacobi Method for a Simple Resonance""; "" 3.1. Notation and assumptions""; "" 3.2. Formal solutions and the Hamiltonâ€?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 ""