Linearization of Impulsive Differential Equations with Ordinary Dichotomy

Abstract

This paper presents a linearization theorem for the impulsive differential equations when the linear system has ordinary dichotomy. We prove that when the linear impulsive system has ordinary dichotomy, the nonlinear system x˙(t)=A(t)x(t)+f(t,x), t≠tk, Δx(tk)=A~(tk)x(tk)+f~(tk,x), k∈ℤ, is topologically conjugated to x˙(t)=A(t)x(t), t≠tk, Δx(tk)=A~(tk)x(tk), k∈ℤ, where Δx(tk)=x(tk+)-x(tk-), x(tk-)=x(tk), represents the jump of the solution x(t) at t=tk. Finally, two examples are given to show the feasibility of our results.