ON A CONNECTION BETWEEN KAM AND NEKHOROSHEVS THEOREMS

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