Stickiness of Trajectories in a Perturbed Anosov System

We consider a perturbation of the Anosov-type system, which leads to the appearance of a hierarchical set of islands-around-islands. We demonstrate by simulation that the boundaries of the islands are sticky to trajectories. This phenomenon leads to the distribution of Poincare recurrences with power-like tails in contrast to the exponential distribution in the Anosov-type systems.