Continuous time random walk model for standard map dynamics

In standard map dynamics, the time series x(t) are analyzed for chaotic orbits bounded by Kolmogorov-Arnold-Moser barriers, for subcritical values of the stochasticity parameter. They can be described as a succession of rather regular oscillations of bounded amplitude in basins located near island chains, and of jumps between basins, at ''random'' times. This motion can be adequately modeled by a continuous time random walk, using values of the parameters taken from the numerical data. The resulting theory describes a subdiffusive motion, for which the mean square displacement tends towards a saturation value.