Statistics of Poincaré recurrences in nonautonomous chaotic 1D map

The statistics of Poincaré recurrences is studied numerically in a one-dimensional cubic map in the presence of harmonic and noisy excitations. It is shown that the distribution density of Poincaré recurrences is periodically modulated by the harmonic forcing. It is substantiated that the theory of the Afraimovich–Pesin dimension can be applied to a nonautonomous map for both harmonic and noisy forcings. It is demonstrated that the relationship between the AP-dimension and Lyapunov exponents is violated in the nonautonomous system.