Internal Arnold diffusion and chaos thresholds in coupled symplectic maps

Abstract

The authors investigate numerically how typical trajectories fill the phase space in low-dimensional symplectic (Hamiltonian) maps with finite phase space. They do not find any sign of a 'chaos threshold' as reported by other authors when the non-linearity parameters are increased. Instead, as expected from Arnold diffusion, they find that single trajectories fill most (if not all) of the coarse-grained phase space even for very small non-linearities. Due to the 'stickiness' of tori also observed in two-dimensional maps, this filling is much slower than what one might expect naively and is possibly described by power laws. The 'chaos threshold' observed in a previous paper is explained as a trivial effect.