一类扰动的三次向量场的分枝

Bifurcations in a Class Perturbed Cubic Vector Field

本文用分析方法系统地研究了一类扰动三次向量场各种可能的极限环与奇异环分布,得到了较完整的结果,这对研究弱化的Hilbert第十六问题以及进一步认识三次向量场的分枝性质都是有意义的。

This paper deals with a class of perturoation of a cubic vector field. Using analytic method,a variety of possible homoclinic and heteroclinic bifurcations and poincare bifurcations of limit cycles are obtained. These results are helpful to the study of the 16th weakened problem of Hilbert.