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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