03700nam 2200601 450 991048052310332120170816143306.01-4704-0373-0(CKB)3360000000464959(EBL)3114426(SSID)ssj0000889125(PQKBManifestationID)11523070(PQKBTitleCode)TC0000889125(PQKBWorkID)10875171(PQKB)10828108(MiAaPQ)EBC3114426(PPN)195416619(EXLCZ)99336000000046495920030108d2003 uy| 0engur|n|---|||||txtccrOn the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems /P. Lochak, J.-P. Marco, D. SauzinProvidence, Rhode Island :American Mathematical Society,2003.1 online resource (162 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 775"Volume 163, number 775 (second of 5 numbers)."0-8218-3268-9 Includes bibliographical references.""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""""Â 2.5. Persistence of tori, invariant manifolds and homoclinic trajectories""""Â 2.6. Splitting and stability""; ""Chapter 3. The Hamiltonâ€?Jacobi Method for a Simple Resonance""; ""Â 3.1. Notation and assumptions""; ""Â 3.2. Formal solutions and the Hamiltonâ€?Jacobi algorithm""; ""Â 3.3. Convergence and domains of analyticity""; ""Â 3.4. Exponential closeness of the invariant manifolds""; ""Â 3.5. Linear versus nonlinear splitting""; ""Â 3.6. Some variants and possible generalizations""; ""Â 3.7. A short historical tour and some concluding remarks""""Appendix. Invariant Tori With Vanishing or Zero Torsion""""Bibliography ""Memoirs of the American Mathematical Society ;no. 775.Hamiltonian systemsInvariant manifoldsElectronic books.Hamiltonian systems.Invariant manifolds.510 s514/.74Lochak P(Pierre),52270Marco J.-PSauzin D.1966-MiAaPQMiAaPQMiAaPQBOOK9910480523103321On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems2262665UNINA