ABSTRACT
Abstract : For a system of ordinary differential equations defined on the direct product of a torus and Euclidean space and subjected to impulsive action on submanifold of codimension 1 of the torus , we study the problem of existence of a piece wise smooth invariant set . For linearized impulsive system a concept of exponential dichotomy is introduced . We prove that the exponential dichotomy is not destroyed by small perturbations of right hand sides of the system.
