Invariant KAM tori and global stability for Hamiltonian systems

We point out a deep connection between KAM theorem and Nekhoroshev's theorem. Precisely, we reformulated the construction by Arnold of the set of invariant tori using Nekhoroshev's theorem as a basic tool. We prove in this way the existence of a hierarchic structure of nested domains characterized by a diffusion speed exponentially decreasing at each step. The set of KAM tori appears as the domain characterized by vanishing diffusion speed.