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. It is shown that the obtained numerical data fully conform to the theoretical results. It is demonstrated that the Poincare recurrence theory can be applied to diagnose.