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On the Existence of Drifting Orbits for Non-Convex Hamiltonian Systems (1505.03969v2)
Published 15 May 2015 in math.CA and math.DS
Abstract: 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 $O(\epsilon)$ can be arbitrarily small. The first drifts occur in a period of time $O(1/\epsilon)$ and then reoccur with frequencies independent of $\epsilon$. We also perform numerical simulations to compare the effects of two conditions for instability in two four-dimensional examples with random parameters.