一类多项式系统无穷远点的中心-焦点判定

Determination of Center-focus at Infinity for a Class of Polynomial System

研究了一类十一次多项式微分系统无穷远点的中心-焦点判定问题.首先通过同胚变换和复变换将系统的无穷远点化为复域中的初等原点,然后在计算机上用Mathematica推导出了新系统原点的前15个奇点量,从而导出了无穷远点为中心和最高阶细焦点的条件.

In this paper, determination of center-focus at infinity for a class of eleven degree polynomial differential system is investigated. Firstly, infinity is transformed into an elementary origin of a complex system by a homeomorphie transformation and a complex transformation.With the help of Mathematica, the first 15 singular point quantities at the origin of the transformed system are deduced.Therefore, the conditions for infinity to be a center and highest order fine focus are obtained.