Numerical evidence of fast diffusion in a three-degree-of-freedom Hamiltonian system with a saddle-center

Abstract

Arnold diffusion is a complicated phenomenon resulting from the presence of a transition chain of whiskered invariant tori. It is very slow and subtle behavior but it is believed to give a central mechanism for long-time instability in multi-degree-of-freedom, near-integrable Hamiltonian systems. Recently, it was shown that similar but fast behavior can also occur in Hamiltonian systems which are not near-integrable but possess saddle-centers. We provide a numerical evidence of this fast diffusion for a three-degree-of-freedom system.