Some stability results on nearly–integrable systems (with dissipation)

Abstract

The stability of nearly–integrable systems can be studied over different time scales and with different techniques. In this paper we review some classical methods, like the averaging technique, the classical perturbation theory, KAM theorem and Nekhoroshev’s stability for exponential times. We investigate also conformally symplectic systems, in particular nearly–integrable systems with dissipation, and we present some results about KAM and exponential stability in the dissipative context.