摘要
本文首先分析了平面自治系统各种奇点邻域的轨线特征 ;接着讨论了高阶奇点邻域轨线与系统特征方程的关系。证明了系统的特征方程满足一定条件时 ,系统的奇点一定不是中心 ,系统的特征方程无实时 ,奇点可能是中心 。
This paper first analyzes the characteristics of path curve of the singular point's neighbo(u)rhood of a plane autonomous system, and then discusses relations between the path curves and the characteristic equation. and proves that the singular point is not a center if the characteristic equation is satisfied some conditions and is probably a center if there is not real root in the characteristic equation, finally gives two judgment methods by which the singular point is judged a center.
