一类平面五次系统的定性分析

Qualitative Analysis for a Planar Quintic System

本文研究平面五次系统（１．１），应用［４，５］的最新结果，给出了奇点Ｏ（０，０）为中心的充要条件和焦点量公式，以及（１．１）至多有一个，二个极限环的充分条件．

In this paper, we study a class of a planar quintic system (1.1) .With the new result of papers [4,5], we obtains the necessary and sufficient conditions under which O(0,0) is a center of (1,1).focus valus of each order at O(0,0)and sufficient conditions under which (1. 1) these exist only one or only two limit cycles.