  We prove a perturbation theorem for the $k$-jets, $k\geq 2$, of the
Poincar\'e map of a closed orbit of the Hamiltonian flow of a Tonelli
Hamiltonian $H: T^*M\to \R$, on a closed manifold $M$. As a consequence we
obtain Ma\~n\'e generic properties of Hamiltonian and Lagrangian flows.
