14473 Potsdam, Germany
Potsdam Institute for Climate Impact Research
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
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.