  Time evolution of a perturbed thermal state is studied in a
quantum-mechanical system with O(N) symmetry. In the limit of large N, time
dependence of O(N)-singlet expectation values can be described by classical
equations of motion in a one-dimensional potential well. Time dependence of the
perturbation is then described by a linear differential equation with
time-dependent periodic coefficient. This equation, depending on the
parameters, admits either exponentially growing/decaying or periodically
oscillating solutions. It is demonstrated that only the latter possibility is
actually realized, thus in such a system there is no redistribution of initial
perturbation over all N degrees of freedom.
