Hiroshi Tamura and Valentin A.Zagrebnov Dynamics of an Open System for Repeated Harmonic Perturbation (97K, LaTeX) ABSTRACT. We use the Kossakowski-Lindblad-Davies formalism to consider an open system defined as the Markovian extension of one-mode quantum oscillator S perturbed by a piecewise stationary harmonic interaction with a chain of oscillators C. The long-time asymptotic behaviour of various subsystems of S +C are obtained in the framework of the dual W -dynamical system approach.