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On the Existence of Drifting Orbits for Non-Convex Hamiltonian Systems

We show the existence of drifting orbits for certain perturbations of non-convex Hamiltonian systems with several degrees of freedom. These orbits remain in the vicinity of resonant surfaces where the action variables can undergo changes $O(1)$ infinitely often although the size of perturbations $O(ε)$ can be arbitrarily small. The first drifts occur in a period of time $O(1/ε)$ and then reoccur with frequencies independent of $ε$. We also perform numerical simulations to compare the effects of two conditions for instability in two four-dimensional examples with random parameters.