Journal of Statistical Physics, Vol. 44, 293-338, 1986

Authors: Giancarlo Benettin and Giovanni Gallavotti

Title Stability of Motions near Resonances in Quasi-Integrable Hamiltonian Systems :

Abstract: Nekhoroshev's theorem on the stability of motions in quasi-integrable Hamiltonian systems is revisited. At variance with the proofs already available in the literature, we explicitly consider the case of weakly perturbed harmonic oscillators; furthermore we prove the confinement of orbits in resonant regions, in the general case of nonisochronous systems, by using the elementary idea of energy conservation instead of more complicated mechanisms. An application of Nekhoroshev's theorem to the study of perturbed motions inside resonances is also provided.

Key words:  Resonances; perturbation theory; KAM theory; Hamiltonian systems
Giovanni Gallavotti
Dipartimento di Fisica, INFN
Universita' di Roma "La Sapienza"
P.le A. Moro 2
I 00185 Roma, Italia