一类五次系统的中心焦点判定

On the Decision Problem of the Center or Focus for a class of 5th Differential System

给出五次系统x=λx-y+yR_2+xR_4,y=x+λy-xR_2+yR_4,R_2=b_1x^2++b_2xy+B_3y^2,R_4=a_4x^4+a_2x^3y+a_1xy^3+a_0y^4,在O(0,0)的各阶焦点量和O为中心的充要条件.

This paper considerc 5th differential system x = λx-y+yR2+xR4,y=x+λy-xR2+yR4, where Rt=b1X2+b2xy+b3y2,R4=a4X4+a3x3y+a1xy3+a0y4,we give the focal valu with order k,k=0,… 4,and necessary and sufficient conditions in which O(0,0) is center of the system.