Hierarchical structures in the phase space and fractional kinetics: I. Classical systems

Abstract

Hamiltonian chaotic dynamics is not ergodic due to the infinite number of islands imbedded in the stochastic sea. Stickiness of the islands' boundaries makes the wandering process very erratic with multifractal space-time structure. This complication of the chaotic process can be described on the basis of fractional kinetics. Anomalous properties of the chaotic transport become more transparent when there exists a set of islands with a hierarchical structure. Different consequences of the described phenomenon are discussed: a distribution of Poincaré recurrences, characteristic exponents of transport, nonuniversality of transport, log periodicity, and chaos erasing. © 2000 American Institute of Physics.