一类三次Lienard系统中心焦点的判定

Criterions of Center and Focus for a Class of Cubic Lienard System

本文研究一类三次Lienard系统(*)的中心焦点判定,按该系统所含参数的一切可能情形分类讨论,导出了计算焦点量的最简公式,核实了细焦点的最大可能阶数,并获得了原点o是中心的充要条件,因此彻底解决了Lienard系统(·)的中心焦点判定问题.

This paper studies criterions of center and focus for a Class of Cubic Lienard system(*). All the possibilities of the system parameters are dicussed. The simplest formula describing the focal values is achieved. The maximum possibl order the fine focus is verified. The necessary and sufficient condition for determining center is obtained. Therefore, the prodlem of how to distingush between center and focus for the Lienard system(*)is completly solved.