Abstract
We consider nonisochronous, 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)ln(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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