Fractal Diffusion in Smooth Dynamical Systems with Virtual Invariant Curves

Abstract

Preliminary results of extensive numerical experiments on a simple model specified by the smooth canonical strongly chaotic 2D-map with global virtual invariant curves (VICs) are presented and discussed. We focus on the statistics of the diffusion rate of individual trajectories in dependence on the model parameters. Our previous conjecture about the fractal statistics determined by the critical structure of both the phase space and the motion is confirmed and studied in some detail. Particularly, we have found specific characteristics of what we termed the VIC diffusion suppression which is related to a new type of the critical structure. An example of ergodic motion with a surprising "hidden" critical structure strongly affecting the diffusion rate was also encountered and discussed.