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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
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
Citation:
G. M. Zaslavsky, M. Edelman, “Stickiness of trajectories in a perturbed Anosov system”, Regul. Chaotic Dyn., 11:2 (2006), 329–336
Linking options:
https://www.mathnet.ru/eng/rcd679 https://www.mathnet.ru/eng/rcd/v11/i2/p329
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