  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 $k = 2n$.
