Multifractality, stickiness, and recurrence-time statistics

Abstract

We identify the fine structure of resonance islands and the stickiness in chaos through recurrence time statistics (RTS), which is based on the concept of Poincar e recurrences. The projection of recurrence time statistics onto the phase space does give relevant information on the hierarchical andmicrostructures of the chaotic beach around the islands of a near-integrable system, the annular billiard. These microstructures interfere in the effective transport of a particle in the phase space, which can be observed through RTS. This technique proves also to be a powerful tool to describe the homoclinic tangle of the manifolds within the chaotic sea.