平面二次系统不存在三次代数曲线鞍结分界线环

Non-existence of the Cubic Algebraical Saddle-node Separatrix-loop in the Planar Quadratic System

本文证明了平面二次系统不存在三次代数曲线鞍结分界线环,从而纠正了沈伯骞氏断言在三次代数同宿轨上有鞍结点的错误.

In this paper, we show that for the planar quadratic system, it has no the cubic algebraical saddle-node separatrix-loop. This conclusion corrects a mistaken result of Ref. [1], in which the author asserts that there existsa saddle-node point in a cubic algebraical homoclinic orbit.