MENU

You are here

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

TitleDrift in phase space: a new variational mechanism with optimal diffusion time
Publication TypeJournal Article
Year of Publication2003
AuthorsBerti, M, Biasco, L, Bolle, P
JournalJ. Math. Pures Appl. 82 (2003) 613-664
Abstract

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.

URLhttp://hdl.handle.net/1963/3020
DOI10.1016/S0021-7824(03)00032-1

Sign in