Is Arnold diffusion relevant to global diffusion?

Abstract

Global diffusion of Hamiltonian dynamical systems is investigated by using a coupled standard maps. Arnold web is visualized in the frequency space, using local rotation numbers, while Arnold diffusion and resonance overlaps are distinguished by the residence time distributions at resonance layers. Global diffusion in the phase space is shown to be accelerated by diffusion across overlapped resonances generated by the coupling term, rather than Arnold diffusion along the lower-order resonances. The former plays roles of hubs for transport in the phase space, and accelerate the diffusion.