平面二次系统极限环（1，3）分布的讨论

On the(1, 3) Distributions of Limit Cycles of Plane Gaudratic Systems

本文（ａ）对文献［１］中的定理２进行了修正，取消了假设条件Ｖ＿７＞０；（ｂ）对曲线Ｍ（ｓ￣２，ｒ）＝０，Ｊ（ｓ￣２，ｒ）＝０，Ｌ（ｓ￣２，ｒ）＝０，Ｔ（ｓ￣２，ｒ）＝０，ｓ￣２＝ｓ以及ｓ￣２＝ｓ的位置关系进行了讨论，在保证系统（１．１）具有极限环（１，３）分布的情况下，扩大了参数（ｓ，ｒ）的变化范围，并用图示给以清晰说明：（ｃ）讨论了一类具有两个无限远奇点的平面二次系统极限环的（１，３）分布：（ｄ）对系统（１．１）不论它在无限远处出现一个、两个或三个奇点，给出了出现极限环线（１，３）分布的统一处理方法。

In this paper,(a)we revise tbe theorem 2 of reference [1] ,omit the condition V_7>0; (b) we discuss the relative Positions of six curves M(s￣2,)=0,J(s￣2,r)=0～=0, L(s￣2,r)=0,T(s￣2,r)=0,s￣2=s and s￣2=s. Under the condition of the (1,3) distribu-tions of limit cycles, we expand the variable regions of parameters (s,r) and clearly show them in figure; (c)we study the (1,3) distributions of limit cycles of one kind quadratic systems with two singular points at the infinite; and (d)we give a general method to discuss the (1,3) distributions of limit cycles of system (1) whatever there is one, two or three singular points at the infinite.