FRACTAL DESCRIPTION OF ANOMALOUS DIFFUSION IN DYNAMICAL SYSTEMS

Abstract

Anomalous diffusion properties are common in a broad spectrum of systems including dynamical systems. In this paper we review an approach based on Lévy scale-invariant distributions to describe transport in dynamical systems. We introduce the basic ingredients that make the approach useful in describing anomalous diffusion and demonstrate the applicability in the cases of one-dimensional iterated maps and of the standard map.