Upper bounds on Arnold diffusion times via Mather theory

This paper considers five examples of hamiltonian systems for which the existence of Arnold's mechanism for diffusion has been shown. These systems have in common that each of them is the perturbation that couples a number of rotators to a pendulum. The main result is that, for all systems considered and for all suffiently small values of the perturbation paramenter, there are orbits whose action variables have a drift of order one in a time which is inversely proportional to the splitting of the homoclinic whiskers. The paper reviews the necessary results concerning the Hamiltonian and uses them to apply Mather theory to the estimate on the drift. These results are important in veryfying the optimality of Nekhoroshev-type theorems.