具有临界两点异宿环的二次系统

THE QUADRIC SYSTEMS POSSESSING THE CRITICAL HETEROCLINIC CYCLE WITH TWO SADDLE POINTS

本文给出一次系统存在临界两点异宿环的充要条件，并证明二次系统的临界两点异宿环必由双曲线的一支和直线或由椭圆和直线构成，其内部的奇点必是中心．推广所研究的这种系统，本文对［１］中提出的一个公开问题也给出了解答．

This paper gaves the sufficient and necessary condition for the existence for the critical heteroclinic cycle with two saddle points for quadric systems.We proved that among the heteroclinic orbits making up the critical heteroclinic cycle, one must be a hyperbola or an ellipse and the other must be a straight line and the singular point enclosed by the critical heteroclinic cycle must be a center for the quadric system.Generalizing the system studied by this paper, we also gave an answer to the open problem raised by [1].