On integral manifolds of multifrequency oscillatory systems

Conditions are found for the existence of an integral manifold for a nonlinear oscillatory system with slowly varying frequencies, and an algorithm for constructing it is described. A theorem is proved on the conditional asymptotic stability of the integral manifold with respect to a set of initial values for the slow variables. Smoothness is also studied, and bounds on the partial derivatives of the function that describes the integral manifold are obtained.