非线性项无界非自治系统的拓扑线性化

The topological linearization of nonautonomous systems with unbounded nonlinear term

Palm er K J证明了:若h(t,x)有界时,存在Rn→Rn的同胚函数H,将x′=A(t)x+h(t,x)的解映为其线性系统x′=A(t)x的解.为扩展此结论,去掉了h(t,x)有界的限制,指出当h(t,x)具有适当结构时,x′=A(t)x+h(t,x)能被线性化.

Palmer shows that there is a homeomorphim H（ R^n →R^n） sending the solutions of the system x＇ = A（t）x ＋ h（t, x） onto the solutions of its linear system x＇ = A（t）x ifh（t, x） is bounded. In this paper, we omit the limitation that h（t, x） must be bounded and point out that x＇ = A（t）x ＋ h（t, x） can be topologically linearlized when h（t, x） has a proper structure.