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Uspekhi Fizicheskikh Nauk, 2013, Volume 183, Number 10, Pages 1009–1028
DOI: https://doi.org/10.3367/UFNr.0183.201310a.1009 (Mi ufn4518) 		 
This article is cited in 16 scientific papers (total in 16 papers)

REVIEWS OF TOPICAL PROBLEMS

Poincaré recurrence theory and its applications to nonlinear physics

V. S. Anishchenko, S. V. Astakhov

Physics Faculty, Chernyshevsky Saratov State University
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DOI: https://doi.org/10.3367/UFNr.0183.201310a.1009
Abstract: Theoretical results concerning the Poincaré recurrence problem and their application to problems in nonlinear physics are reviewed. The effects of noise, nonhyperbolicity, and the size of the recurrence region on the characteristics of the recurrence time sequence are examined. Relations of the recurrence time sequence dimension to the Lyapunov exponents and the Kolmogorov entropy are demonstrated. Methods for calculating the local and global attractor dimensions and the Afraimovich – Pesin dimension are presented. Methods using the Poincaré recurrence times to diagnose the stochastic resonance and the synchronization of chaos are described.
Received: October 30, 2012
Revised: March 15, 2013
Accepted: March 19, 2013
English version:
Physics–Uspekhi, 2013, Volume 56, Issue 10, Pages 955–972
DOI: https://doi.org/10.3367/UFNe.0183.201310a.1009
Bibliographic databases:
Document Type: Article
PACS: 05.45.-a
MSC: 37B20, 37C45, 37L30
Language: Russian
Citation: V. S. Anishchenko, S. V. Astakhov, “Poincaré recurrence theory and its applications to nonlinear physics”, UFN, 183:10 (2013), 1009–1028; Phys. Usp., 56:10 (2013), 955–972
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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