Jets of closed orbits of Ma\~n\'e generic Hamiltonian flows

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