Topologica Linearization Of Two Kinds Of Differential Systems

This paper studies topological linearization of two kinds of differential systems. The method is based on the existence and uniqueness theorem, fixed point theorem, Bellman differential inequality, and so on. This paper includes three chapters.In chapter1, we briefly introduce the research background and motivation of this dissertation, and possible difficulty appearing due to study of differential systems with piecewise constant argument.In chapter2, we study the linearization of differential systems of with piecewise constant argument which has an exponential dichotomy. We transform the differential systems with piecewise constant argument into difference equation. By Bellman inequality and fixed point theorem, the linearization theorem is proved.In chapter3, we consider the linearization of differential systems if the linear system has a nonuniform exponential dichotomy. Since the nonuniform exponential dichotomy is different from the classical exponential dichotomy, it is necessary to revisit the lineariza-tion theorem.