对于张芷芬定理的一点补记

A Little Complement for ZHANG Zhi - fen Theory

在系统(1)中,当bn≠0,n<m时,奇点O(0,0)是鞍结点,但在更细化的情况下,鞍结点附近的图该 怎样画,张芷芬教授并未给出,本文利用张的方法,根据n的奇偶性,bn,a2m的取值情况,对鞍结点进行更细致的 分类。

In the system(1) ,when 'bn≠0,n< m',the singular point 0(0,0) is a saddle- node,but Pro Zhang didn't give the answer of how to draw the phase portrait near the saddle- node,in the more accurate conditions.In this paper,author use Zhang's method,according to the odevity of n and different value of bn, a2m, cany on the more careful classification to the saddle - node.