Izvestiya of Saratov University.
ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

Afraimovich–Pesin dimension

Statistics of Poincare Recurrence with Considering Effect of Fluctuations

The basic statistical characteristics of Poincare recurrence are obtained numerically for the logistic map in a chaotic regime. The mean values, variation and recurrence distribution density are calculated and their dependence on a return size is analysed. Afraimovich–Pesin dimension values are obtained. It is verified that the Afraimovich–Pesin dimension corresponds to the Lyapunov exponent. the peculiarities of the influence of noise on the recurrence statistics are studied in local and global approaches.

Poincare Recurrences and Afraimovich–Pesin Dimension in a Nonautonomous Conservative Oscillator

Background and Objectives: One of the fundamental features of the temporal dynamics is Poincare recurrence. It have been shown that statistics of return time in global approach depends on topological entropy h. The case of h > 0 (set with mixing) has been already studied theoretically. The theoretical conclusions have been confirmed by numerical simulation. The case of the sets without mixing (h = 0) has been studied theoretically, but recent numerical results shows some special aspects which are absent in theory.