Statistics of return times in a self-similar model

In this paper, we propose a model for the hyperbolic part of the phase spac e of a Hamiltonian system that is located near a hierarchical islands aroun d islands structure. We study the statistics of Poincare recurrences, the t ype of orbits that are mainly responsible for slowly decaying correlations, and thus the mechanisms generating power law tails. (C) 1999 American Inst itute of Physics. [S1054-1500(99)00203-7].