Journal ArticleDOI
On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems
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The Hamiltonian Symplectic geometry and the splitting of invariant manifolds have been studied in this article, where the splitting matrix is estimated by the Hamilton-Jacobi method for a simple resonance.Abstract:
Introduction and some salient features of the model Hamiltonian Symplectic geometry and the splitting of invariant manifolds Estimating the splitting matrix using normal forms The Hamilton-Jacobi method for a simple resonance Appendix. Invariant tori with vanishing or zero torsion Bibliography.read more
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Journal ArticleDOI
Geometric properties of the scattering map of a normally hyperbolic invariant manifold
TL;DR: In this article, it was shown that the scattering map is symplectic (resp. exact symplectic) when f and are symplectic and the primitive function is a variational interpretation as dierence of actions.
Journal ArticleDOI
Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems
Jean-Pierre Marco,David Sauzin +1 more
TL;DR: In this article, the stability of action variables for Gevrey quasi-convex near-integrable Hamiltonian systems was studied, and it was shown that 1/2nα is the optimal exponent for the time of stability and b = 1 2n as an exponent for radius of confinement of the action variables.
Journal ArticleDOI
A functional analysis approach to Arnold diffusion
TL;DR: In this paper, a functional analysis approach to the splitting of separatrices and shadowing problem for nearly integrable partially isochronous Hamiltonian systems is presented. But this approach is not suitable for the case of nearly-integrable systems.
Journal ArticleDOI
Speed of Arnold diffusion for analytic Hamiltonian systems
TL;DR: For a convex, real analytic, e-close to integrable Hamiltonian system with n ≥ 5 degrees of freedom, the authors constructed an orbit exhibiting Arnold diffusion with the diffusion time bounded by
Journal ArticleDOI
Oscillatory motions for the restricted planar circular three body problem
TL;DR: In this paper, it was shown that for any value of the mass ratio, there exist transversal intersections between stable and unstable manifolds of infinity in the level sets of the Jacobi constant.
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