On the problem of stability for near to integrable Hamiltonian systems
by Antonio Giorgilli

Abstract: 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.

Proceedings of the International Congress of Mathematicians Berlin 1998, Vol. III, Documenta Mathematica, extra volume ICM 1998, 143--152 (1998)

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