Creation of periodic points of all types in the neighborhood of Kolmogorov-Arnold-Moser tori

We prove in this paper that there exists a residual subset G of the set of C-infinity symplectic diffeomorphisms of a manifold M such that : for all f in G, every Lagrangian periodic torus (with period tau) on which f(tau) is conjugated to an ergodic rotation is limit of periodic points of all types (i. e. which have hyperbolic and elliptic dimensions that we can chose).