Quasi-periodic motions on symplectic tori

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 \(n \leq k < 2n \). In this paper, we extend this result to the case of a quasi-periodic motion on symplectic tori \(k = 2n\).