Differential systems, the mapping over period for which is represented by a product of three exponential matrixes

For some periodic differential systems the sufficient conditions of a representation of the mapping over period as a product of a three exponential matrix of the special aspect are obtained. Obtained results are used for research of problems of the existence and stability of periodic solutions of nonlinear systems and the asymptotic orbital stability of cycles of autonomous differential systems. © 2006 Elsevier Inc. All rights reserved