2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80358The 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.LaTeX, 14 pagesChaotic Dynamics70K55 (Primary) 34F05, 34K50, 37H10, 37L55 (Secondary)text