Massimiliano Berti, Luca Biasco, Philippe Bolle
Optimal stability and instability results
for a class of nearly integrable Hamiltonian system
(255K, PS)
ABSTRACT. 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.