Optimal stability and instability results for a class of nearly integrable Hamiltonian systems

Details Optimal stability and instability results for a class of nearly integrable Hamiltonian systems Optimal stability and instability results for a class of nearly integrable Hamiltonian systems

2002-03-19

arxiv.org/abs/math/0203188v1

Mathematics

Dynamical Systems

6 pages

Scientific paper

We consider a nearly integrable, non-isochronous, a-priori unstable Hamiltonian system with a (trigonometric polynomial) $O(\mu)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time $T_d = O((1/ \mu) \log (1/ \mu))$ by a variational method which does not require the existence of ``transition chains of tori'' provided by KAM theory. We also prove that our estimate of the diffusion time $T_d$ is optimal as a consequence of a general stability result proved via classical perturbation theory.

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