Reflecting function and periodic solutions of differential systems with small parameter

Abstract

The aim of this paper is to combine the method of reflective function and the perturbation method. The set of a linear differential systems, the reflecting matrix for which is represented by a product of three exponential matrixes is allocated. It has allowed to obtain the sufficient conditions of existence of a family of periodic solutions close to a given solution of multidimensional nonlinear differential systems. Obtained results are illustrated by examples.