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Regular and Chaotic Dynamics, 2006, Volume 11, Issue 2, Pages 329–336
DOI: https://doi.org/10.1070/RD2006v011n02ABEH000356 (Mi rcd679) 		 
On the 70th birthday of L.P. Shilnikov

Stickiness of trajectories in a perturbed Anosov system

G. M. Zaslavskyab, M. Edelmana

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
DOI: https://doi.org/10.1070/RD2006v011n02ABEH000356
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.
Received: 19.09.2005
Accepted: 13.11.2005
Bibliographic databases:
Document Type: Article
MSC: 37Dxx, 37Mxx
Language: English
Citation: G. M. Zaslavsky, M. Edelman, “Stickiness of trajectories in a perturbed Anosov system”, Regul. Chaotic Dyn., 11:2 (2006), 329–336
Citation in format AMSBIB
\Bibitem{ZasEde06}
\by G. M. Zaslavsky, M. Edelman
\paper Stickiness of trajectories in a perturbed Anosov system
\jour Regul. Chaotic Dyn.
\yr 2006
\vol 11
\issue 2
\pages 329--336
\mathnet{http://mi.mathnet.ru/rcd679}
\crossref{https://doi.org/10.1070/RD2006v011n02ABEH000356}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2245087}
\zmath{https://zbmath.org/?q=an:1164.37315}
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