一类五次多项式系统无穷远点的极限环(英文)

Limit cycles of infinity in a quintic polynomial system

运用一种间接的方法研究了一类五次平面多项式系统无穷远点的极限环分支问题.首先将该问题转换成在原点的极限环分支问题,然后通过奇点量的计算,推导出系统在原点(无穷远点)的最高阶细焦点的条件,首次证明了五次多项式系统可在无穷远点分支出九个极限环.

In this paper,an indireet method is used to study the bifnrcations of limit cycles at infinity for a class of quintic polynomial system.in which the problem for bifureations of limit cycles at infinity is transferred into that at the origin.By the computation of singular poiot values,the conditions of the origin（correspondingly infinity）to be a center and the highest degree fine focus are derived .Fially,it is showed firstly that q quintic differential system can bifurcate nine limit eyeles at infinity.