R^n中似梯度型系统异缩轨的存在性

Heteroclinic orbits of gradient-like systems in R^n

本文讨论Ｒ~ｎ中似梯度型系统，证明了三种吸引子的等价性并给出判别异缩轨存在的一个准则．

This paper is concerned with the orbits connecting isolated critical points of gradient-like systems in R^n. A criterion to judge the existence of connecting orbits is given,and furthermore, if the two isolated critical points are attractor and repeller respectively,the set composed of connecting orbits is an open and unbounded set.