全对称2n-1次系统的中心焦点与极限环分支

Center or focus and limit cycles bifurcation on a class of 2n-1 degrees symmetrical system in the whole plane

本文研究了全对称2n-1次系统,求出了原点的前n-1阶焦点量,得出了该系统的中心条件及它在整个相平面上最多可扰动出n-1个小振幅极限环.

In this paper, a class of 2n-1 degrees symmetrical system in the whole plane is investigated.By the comp.utation of focal value,we prove that the system has n-1 limit cycles in the whole plane at most.At the same time,the central condition in the origin i., obtained.