G. M. Zaslavsky, M. Edelman, “Stickiness of trajectories in a perturbed Anosov system”, Regul. Chaotic Dyn., 2006, Volume 11, Issue 2,Pages <nobr>329

On the 70th birthday of L.P. Shilnikov

Stickiness of trajectories in a perturbed Anosov system

G. M. Zaslavsky^ab, M. Edelman^a

^a Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012, USA
^b Department of Physics, New York University, 2-4 Washington Place, New York, NY 10003, USA

Abstract: 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 Poincaré recurrences with power-like tails in contrast to the exponential distribution in the Anosov-type systems.

Keywords: Anosov systems, sticky trajectories, Poincaré recurrences.

MSC: 37Dxx, 37Mxx

Received: 19.09.2005
Accepted: 13.11.2005

Language: English

DOI: 10.1070/RD2006v011n02ABEH000356