TY  - BOOK
AU  - Lochak,P.
AU  - Marco,J.-P.
AU  - Sauzin,D.
TI  - On the Splitting of Invariant Manifolds in Multidimensional Near-Integrable Hamiltonian Systems
T2  - Memoirs of the American Mathematical Society
SN  - 9781470403737
AV  - QA614.83 -- .L63 2003eb 
U1  - 510 s;514/.74 
PY  - 2003///
CY  - Providence
PB  - American Mathematical Society
KW  - Hamiltonian systems
KW  - Invariant manifolds
KW  - Electronic books
N1  - Intro -- 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 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
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114426
ER  -