золотое сечение

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

Authors: Galaktionova T. I., Semenova N. I., Anishchenko V. S.

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.

Investigating Stationary Conditions for Moments of Stochastic Process, Driven by Multiplicative Dichotomous Noise and Featuring Erlang First-order Distribution Function, Conditions Related by Golden Ratio

Authors: Sirotkin O. L.

Conditions for the existence of stationary moments of a stochastic process, satisfying a linear differential stochastic first-order equation, comprising a coefficient, subjected to non-Markov dichotomous noise fluctuations with an arbitrary correlation time, are investigated. It is shown that the existence of stationary moments is related to the golden ratio tying the parameters of the dynamic system and dichotomous noise.