具特定奇点分布的一个三次系统

A Cubic System with Special Distribution of Critical Point

给出了一个具体的三次系统 ,它的有限远奇点中有四个构成一凹四边形 ,三个外顶点为焦点 ,而另一个内顶点为鞍点 .这是二次系统所不能出现的结构 .这一具体实例证明了文 [1]中的一个猜测 .

The paper gives a concrete cubic system which has 6 finite critical points.Four of them form the vertices of a concave quadrilateral,among which 3 outer vertices are foci,1 inner vertex is a saddle.This distribution is impossible for the quadratic system.The numerical example proves the conjecture of [1].