Linearization of impulsive differential equations with ordinary dichotomy - Wong, P. J. Y. (2014)
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≠t_k, ∆x(t_k )= A ̃(t_k )x(t_k )+ f ̃(t_k,x), k∈Z is topologically conjugated to x ̇(t)=A(t)x(t), t≠t_k, ∆x(t_k )= A ̃(t_k )x(t_k ), k∈Z, where ∆x(t_k )=x(t_k^+ )-x(t_k^-), x(t_k^- )= x(t_k), represents the jump of the solution x(t) at t= t_k. Finally, two examples are given to show the feasibility of our results.