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

Hamiltonian chaotic dynamics is not ergodic due to the infinite number of i slands imbedded in the stochastic sea. Stickiness of the islands' boundarie s makes the wandering process very erratic with multifractal space-time str ucture. This complication of the chaotic process can be described on the ba sis of fractional kinetics. Anomalous properties of the chaotic transport b ecome more transparent when there exists a set of islands with a hierarchic al structure. Different consequences of the described phenomenon are discus sed: a distribution of Poincare recurrences, characteristic exponents of tr ansport, nonuniversality of transport, log periodicity, and chaos erasing. (C) 2000 American Institute of Physics. [S1054-1500(00)01301-X].