Drift in phase space: a new variational mechanism with optimal diffusion time

Details Drift in phase space: a new variational mechanism with optimal diffusion time Drift in phase space: a new variational mechanism with optimal diffusion time

2002-05-29

arxiv.org/abs/math/0205307v1

Mathematics

Functional Analysis

34 pages

Scientific paper

We consider non-isochronous, nearly integrable, a-priori unstable Hamiltonian systems 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 derived from classical perturbation theory.

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