Arnold's Diffusion in nearly integrable isochronous Hamiltonian systems

Details Arnold's Diffusion in nearly integrable isochronous Hamiltonian systems Arnold's Diffusion in nearly integrable isochronous Hamiltonian systems

2000-11-02

arxiv.org/abs/math/0011017v1

Mathematics

Dynamical Systems

32 pages

Scientific paper

We consider the problem of Arnold's diffusion for nearly integrable isochronous Hamiltonian systems. We prove a shadowing theorem which improves the known estimates for the diffusion time. We also develop a new method for measuring the splitting of the separatrices. As an application we justify, for three time scales systems, that the splitting is correctly predicted by the Poincar\'e-Melnikov function.

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