非自治系统全局线性化

Global Linearization of Nonautonomous System

Ｐａｌｍｅｒ〔１〕在ｆ满足有界及李普希兹条件的前提下，将Ｈａｒｔｍａｎ〔２〕的线性化理论推广到非自治系统．本文进一步考虑ｆ无界及李氏系数为ｒ（ｔ）的情形，ｒ（ｔ）满足∫ｔ＋１ｔｒ（ｓ）ｄｓ≤ｃ，ｃ为正常数，得到了同样的结果，从而推广了文［１］的主要定理．

As the most important subject of ordinary differential equations and dynamical systems, the linearization of nonlinear system has been studied by many people. Palmer generalized Hartman′s linearization theorem to nonautonomous systems. In this paper, we obtain the same result in spite of the fact that the conditions of their theorem are weaken.