finite object point

Suppose the system has are only one finite singular point(0,0),then we can assume b_(50)=0,which special directions are determined by equation G(θ)=0,introduce Poincare transformation to discuss infinite singular points,according to the.

研究了一类平面齐五次系统dxdxdt=a50x5+a41x4y+a32x3y2+a23x2y3+a14xy4+a05y5,dydt=b50x5+b41x4y+b32x3y2+b23x2y3+b14xy4+b05y5当其只有唯一的有限远奇点且具有三对特殊方向时的全局拓扑结构及系数条件。

Global topological classification and its coefficient conditions of a kind of plane homogeneous fifth system with four special direction are obtained by researching the structure of infinite singular point and the type of rays of passing the only finite singular point O(0,0).

通过研究一类具有四对特殊方向的平面齐五次系统的无穷远奇点的结构和过唯一有限远奇点O(0,0)的射线的类型,得出其全局拓扑分类及相应的系数条件。

The relationship among finite singular point, infinite singular point and linear solution in the complex plane is discussed.

本文研究平面N次系统x =x +Pn(x ,y) ,y =Qn(x ,y) ,这里Pn(x ,y) ,Qn(x ,y)为N次多项式齐式 ,讨论了有限远奇点、无限远奇点和直线解三者之间在复平面内的关系 。