【摘要】 微分方程dx/dt=Ax +f(x)(其中A的特征根实部异于零)拓扑线性化的经典结论是由Hartman与 Grobman给出的,但是他们的结论都是局部拓扑线性化,即要求同胚函数限制在原点的小邻域内．如 果要延伸到全局上的话,必须f(x)有界．本文研究了系统(1．3),证明当此系统满足适当的条件时可全 局线性化．更多还原

【Abstract】 The classical conclusions of topological linearization of the differential equation dx/dt= Ax +f(x) (none of the eigenvalues of A has zero real part) are given by Hartman and Grobman. But, their conclusion are only limited to the small neighborhood of origin. If the system can be globally linearizied, then f(x) must be bounded. In this paper, we consider the system (2.1), point out that the system can be topological linearlized under some conditions. Then, we can obtain more general conclusion.更多还原