On a connection between KAM and Nekhoroshev's theorem
by Alessandro Morbidelli and Antonio Giorgilli

Abstract: Using the iteration of Nekhoroshev's theorem as a basic tool, we point out the existence of a hierarchic structure of nested domains underlying the phenomenon of diffusion. At each level we find that the diffusion speed is exponentially small with respect to the previous level. The set of KAM tori is the domain characterized by a zero diffusion speed.

Physica D 86, 514-516 (1995)

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