Superexponential stability of KAM tori
by Alessandro Morbidelli and Antonio Giorgilli

Abstract: We study the dynamics in the neighbourhood of an invariant torus of a nearly integrable system. We provide an upper bound to the diffusion speed, which turns out to be of superexponentially small size $\exp(-\exp(1/\rho))$, $\rho$ being the distance from the invariant torus. We also discuss the connection of this result with the existence of many invariant tori close to the considered one.

J. Stat. Phys. 78, 1607-1617 (1995)

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