Jürgen Kurths

Address: 14473 Potsdam, Germany

E-mail: kurths@pik-potsdam.de

University: Potsdam Institute for Climate Impact Research

Publications:

Anishchenko V. S., Astakhov S. V., Boev Y. I., Kurths J.

Poincaré recurrences in a system with non-strange chaotic attractor
2012, Vol. 8, No. 1, pp. 29-41

Abstract

Statistical properties of Poincaré recurrences in a two-dimensional map with chaotic non-strange attractor have been studied in numerical simulations. A local and a global approaches were analyzed in the framework of the considered problem. It has been shown that the local approach corresponds to Kac’s theorem including the case of a noisy system in certain conditions which have been established. Numerical proof of theoretical results for a global approach as well as the Afraimovich–Pesin dimension calculation are presented.

Keywords: Poincaré recurrence, attractor dimension, Afraimovich–Pesin dimension

Citation: Anishchenko V. S., Astakhov S. V., Boev Y. I., Kurths J., Poincaré recurrences in a system with non-strange chaotic attractor, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 1, pp. 29-41

DOI:10.20537/nd1201002

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