Title: On the Problem of Stability for Near to Integrable Hamiltonian Systems

Some recent applications and extensions of Nekhoroshev's theory on exponential stability are presented. Applications to physical systems concern on the one hand realistic evaluations of the regions where exponential stability is effective, and, on the other hand, the relaxation time for resonant states in large, possibly infinite systems. Extensions of the theory concern the phenomenon of superexponential stability of orbits in the neigbourhood of invariant KAM tori.

1991 Mathematics Subject Classification: Primary 58F10; Secondary 70F15, 70H05, 70K20

Keywords and Phrases: Perturbation theory, Nekhoroshev theory, exponential stability.

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