Anomalous diffusion and Lévy statistics in intermittent chaotic systems

Abstract

Deviations from simple Brownian motion have been observed in intermittent chaotic systems; of particular interest has been the case of enhanced diffusion. We review an approach to this anomalous behavior based on L~vy scale-invariant distributions to describe transport in such systems. We introduce the basic ingredients that make the approach useful in describing the non-Brownian behavior and demonstrate the applicability in the cases of the standard map, "egg-crate" potential and a one-dimensional iterated map which shows a combined laminar and dispersive motion.