2002/11/09 by V. V. Zverev
Physics and Astronomy · #nlin.CD #msc:70K55 #msc:34F05 #msc:34K50 #msc:37H10 #msc:37L55
published as Stochastics and Dynamics, Vol. 3, No. 4 (2003) 421-433 · LaTeX, 14 pages
arxiv created 2002/11/09 · arxiv updated 2009/11/30
The statistical behavior of a nonlinear system described by a mapping with phase rotation is studied. We use the Kolmogorov-Chapman equations for the multi-time probability distribution functions for investigation of dynamics under the external noise perturbations. We find a stationary solution in the long-time limit as a power series around a state with complete phase randomization ("phase mixing"). The Ornstein-Uhlenbeck and Kubo-Andersen models of noise statistics are considered; the conditions of convergence of the power expansions are established.