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100   $a20030108d2003      uy|            0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aOn the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems /$fP. Lochak, J.-P. Marco, D. Sauzin
210  1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2003.
215   $a1 online resource (162 p.)
225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 775
300   $a"Volume 163, number 775 (second of 5 numbers)."
311   $a0-8218-3268-9 
320   $aIncludes bibliographical references.
327   $a""Contents""; ""Chapter 0. Introduction and Some Salient Features of the Model Hamiltonian""; ""Chapter 1. Symplectic Geometry and the Splitting of Invariant Manifolds""; ""A? 1.1. Symplectic geometry: a short reminder""; ""A? 1.2. Hyperbolic invariant manifolds""; ""A? 1.3. Angles of Lagrangian planes: the symplectic viewpoint""; ""A? 1.4. Angles of Lagrangian planes: the Euclidean viewpoint""; ""A? 1.5. Symplectic isomorphisms, angles and splitting forms""; ""A? 1.6. The splitting of Lagrangian submanifolds""; ""A? 1.7. Lagrangian submanifolds in a cotangent bundle""
327   $a""A? 1.8. Hyperbolic tori and normally hyperbolic invariant manifolds""""A? 1.9. The perturbative setting""; ""A? 1.10. Lagrangian intersections and homoclinic trajectories""; ""A? 1.11. The splitting of the invariant manifolds of hyperbolic tori""; ""Chapter 2. Estimating the Splitting Matrix Using Normal Forms""; ""A? 2.1. Resonant normal forms""; ""A? 2.2. Computations in the vicinity of a resonant surface""; ""A? 2.3. Splitting in a perturbative setting, variance and stability""; ""A? 2.4. General exponential estimates for the splitting matrix""
327   $a""A? 2.5. Persistence of tori, invariant manifolds and homoclinic trajectories""""A? 2.6. Splitting and stability""; ""Chapter 3. The Hamiltona???Jacobi Method for a Simple Resonance""; ""A? 3.1. Notation and assumptions""; ""A? 3.2. Formal solutions and the Hamiltona???Jacobi algorithm""; ""A? 3.3. Convergence and domains of analyticity""; ""A? 3.4. Exponential closeness of the invariant manifolds""; ""A? 3.5. Linear versus nonlinear splitting""; ""A? 3.6. Some variants and possible generalizations""; ""A? 3.7. A short historical tour and some concluding remarks""
327   $a""Appendix. Invariant Tori With Vanishing or Zero Torsion""""Bibliography ""
410  0$aMemoirs of the American Mathematical Society ;$vno. 775.
606   $aHamiltonian systems
606   $aInvariant manifolds
615  0$aHamiltonian systems.
615  0$aInvariant manifolds.
676   $a510 s
676   $a514/.74
700   $aLochak$b P$g(Pierre),$052270
702   $aMarco$b J.-P
702   $aSauzin$b D.$f1966-
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910788849003321
996   $aOn the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems$93836105
997   $aUNINA