The reducibility property of linear system of differential equations plays a significant role in the theoretical research of asymptotic stability of the system of linear differential equations. In 1892, A.M. Lyapunov proved the reducibility property of linear homogeneous systems of differential equations with periodic coefficients. In 1992, Jorba, A. and Simó, C. proved the reducibility of linear differential equations with quasi-periodic coefficients. Moreover, all periodic functions and all quasi-periodic functions will be semi-periodic functions. In this paper, we consider one new definition of semi periodic functions and consider the reducibility of linear homogeneous systems of differential equations with semi periodic coefficients.

Abstract

The reducibility property of linear system of differential equations plays a significant role in the theoretical research of asymptotic stability of the system of linear differential equations. In 1892, A.M. Lyapunov proved the reducibility property of linear homogeneous systems of differential equations with periodic coefficients. In 1992, Jorba, A. and Simó, C. proved the reducibility of linear differential equations with quasi-periodic coefficients. Moreover, all periodic functions and all quasi-periodic functions will be semi-periodic functions. In this paper, we consider one new definition of semi periodic functions and consider the reducibility of linear homogeneous systems of differential equations with semi periodic coefficients.