Symbolic Dynamics Approach to the Two-Dimensional Chaos in Area-Preserving Maps: A Fractal Geometrical Model

Abstract

The statistical properties of the two-dimensional chaos are studied by taking account of the self-similar hierarchical structure of phase space. The symbolic renewal process is constructed in the framework of the semi-markovian class. The interrelation between the Pareto-Zipf law and the non-stationarity of the area-preserving map is discussed.