Quasi-periodic motions on symplectic tori

Abstract

The results of Kolmogorov, Arnold, and Moser on the stability of quasi-periodic motions spanning lagrangian tori in Hamiltonian systems are of fundamental importance and led to the development of KAM theory. Over the years, many variations of these results on quasi-periodic motions have been considered. In this paper, we present a more conceptual way of attacking such problems by considering the particular case of quasi-periodic motions on symplectic tori.