Perturbation Theorems for a Multifrequency System with Pulses

Abstract

We consider a problem of preservation of a piecewise continuous invariant toroidal set for a class of multifrequency systems with pulses at nonfixed times under perturbations of the right-hand side. New theorems that impose constraints on perturbation terms not in the entire phase space but only in a nonwandering set of the dynamical system guarantee the existence of exponentially stable invariant toroidal set.