Morbidelli, A. & Giorgilli, A. J Stat Phys (1995) 78: 1607. doi:10.1007/BF02180145
We study the dynamics in the neighborhood 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/σ)], σ 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.