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

Massimiliano Berti·Luca Biasco·Philippe Bolle
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Abstract

We consider non-isochronous, nearly integrable, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) $O(μ)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time $ T_d = O((1/ μ) \log (1/ μ))$ 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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Massimiliano Berti, Luca Biasco, Philippe Bolle. 2002-05-29. Drift in phase space: a new variational mechanism with optimal diffusion time. https://arxiv.org/abs/math/0205307

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