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

G. M. Zaslavsky; M. Edelman

doi:10.1063/1.166481

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

Chaos. 2000 Mar;10(1):135-146. doi: 10.1063/1.166481.

Authors

G. M. Zaslavsky¹, M. Edelman

Affiliation

¹ Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012Department of Physics, New York University, 2-4 Washington Place, New York, New York 10003.

PMID: 12779369
DOI: 10.1063/1.166481

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 Poincare recurrences, characteristic exponents of transport, nonuniversality of transport, log periodicity, and chaos erasing. (c) 2000 American Institute of Physics.