论文标题
全球Hartman-Grobman定理
A Global Hartman-Grobman Theorem
论文作者
论文摘要
我们表明，对于双曲线平衡点的任何有限邻域$ x_0 $，有一个转换是局部同构的，因此该系统已更改为该社区的线性系统。 如果$ df（x_0）$的特征值均位于左半复杂平面中，则在整个吸引力区域上存在同构，因此在这种坐标更改下，吸引力区域上的非线性系统被更改为线性系统。
We showed that for any bounded neighborhood of a hyperbolic equilibrium point $x_0$, there is a transformation which is locally homeomorphism, such that the system is changed into a linear system in this neighborhood. If the eigenvalues of $Df(x_0)$ are all located in the left-half complex plane, then there is a homeomorphism on the whole region of attraction such that the nonlinear system on the region of attraction is changed into a linear system under such a coordinate change.
