一个在无穷远点分支出八个极限环的多项式微分系统

本文研究一类高次系统无穷远点的中心条件与极限环分支问题．作者首先推出一个计算系统无穷远点奇点量的线性递推公式，并利用计算机代数系统计算出该系统在无穷远点处的前11个奇点量，从而导出无穷远点成为中心和最高阶细焦点的条件，在此基础上作者首次给出了多项式系统在无穷远点分支出8个极限环的实例。

A POLYNOMIAL DIFFERENTIAL SYSTEM WITH EIGHT LIMIT CYCLES AT INFINITY

In this article,the center conditions and the bifuraction of limit cycles at infinity for a class of polynomial differential systems are investigated.Firstly,the authors give a recursive formula to compute the singular point quantities of the systems.Then,the first eleven singular point quantities bave been computed and the conditions for infinity to be a center have been deduced as well.At last,the authors construct a system that allows the appearance of eight limit cycles in the neighborhood of infinity.It is the first time that an example of polynomial differential system with eight limit cycles bifurcating from infinity is given.