一类3次多项式系统无穷远点的奇点量与中心条件

Singular point quantities and center conditions at the infinity for a class of cubic polynomial system

研究了一类三次多项式系统无穷远点的奇点量与中心条件,用一同胚变换将无穷远点转变成原点(初等奇点),用计算机代数系统Mathematica计算了这个多项式系统无穷远点的前18个奇点量,并得到了无穷远点的中心条件和18阶细焦点的条件.

It was studied the center conditions at the equator of a class of cubic polynomial system with no singular point at the infinity based on the method of a homeomophic transformation of the infinity into the origin （ linear singular point）. The first 18 singular point quantities were computed by Mathematica. At the same time, the conditions for the infinity to be a center were derived respectively.