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

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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 Td = O((1/ μ) (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 Td is optimal as a consequence of a general stability result derived from classical perturbation theory.