Linearization of Impulsive Differential Equations with Ordinary Dichotomy

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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 systemx˙(t)=A(t)x(t)+f(t,x),t≠tk,Δx(tk)=A~(tk)x(tk)+f~(tk,x),k∈ℤ, is topologically conjugated tox˙(t)=A(t)x(t),t≠tk,Δx(tk)=A~(tk)x(tk),k∈ℤ, whereΔx(tk)=x(tk+)-x(tk-),x(tk-)=x(tk), represents the jump of the solutionx(t)att=tk. Finally, two examples are given to show the feasibility of our results.