Reviews of topical problems

Poincaré recurrence theory and its applications to nonlinear physics

Physics Department, Saratov State University named after N.G. Chernyshevsky, ul. Astrakhanskaya 83, Saratov, 410012, Russian Federation

Theoretical results on 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. The relationships of the recurrence time sequence dimension with 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.

Fulltext is available at IOP
PACS: 05.45.−a
DOI: 10.3367/UFNe.0183.201310a.1009
Citation: Anishchenko V S, Astakhov S V "Poincaré recurrence theory and its applications to nonlinear physics" Phys. Usp. 56 955–972 (2013)
BibTexBibNote ® (generic)BibNote ® (RIS) MedlineRefWorks
PT Journal Article
TI Poincaré recurrence theory and its applications to nonlinear physics
AU Anishchenko V S
FAU Anishchenko VS
AU Astakhov S V
FAU Astakhov SV
DP 10 Oct, 2013
TA Phys. Usp.
VI 56
IP 10
PG 955-972
RX 10.3367/UFNe.0183.201310a.1009
SO Phys. Usp. 2013 Oct 10;56(10):955-972

Received: 30th, October 2012, revised: 15th, March 2013, 19th, March 2013

Оригинал: Анищенко В С, Астахов С В «Теория возвратов Пуанкаре и её приложение к задачам нелинейной физики» УФН 183 1009–1028 (2013); DOI: 10.3367/UFNr.0183.201310a.1009

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