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.
Superexponential stability of KAM tori / A. Morbidelli, A. Giorgilli. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 78:5-6(1995 Mar), pp. 1607-1617.
Superexponential stability of KAM tori
A. GiorgilliUltimo
1995
Abstract
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.
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