Quasi-periodic motions on symplectic tori

Abstract

The KAM (Kolmogorov-Arnold-Moser) theorem guarantees the stability of quasi-periodic invariant tori by perturbation in some Hamiltonian systems. Michel Herman proved a similar result for quasi-periodic motions, with $k$-dimensional involutive manifolds in Hamiltonian systems with $n$ degrees of freedom $n\le k<2n$. In this paper, we extend this result to the case of a quasi-periodic motion on symplectic tori $k=2n$.