Z_6等变系统所有可能的相图

Possible Phrase Portraits in Z_6-eqivariant System

简单介绍了 Z6 等变系统的背景 ,利用微分方程的定性理论及分枝理论 ,求出有限平面奇点及无穷远奇点 ;通过特征值方法判断奇点类型 ;根据系统等变性及解的唯一性讨论了在参数空间里所有可能的相图 ,给出了具体的形式 ,一共五类十六个相图 .

This paper simply introduces the background of Z 6-equivariant system. Using qualitative theory and bifurcation theory of differential equation, we seek out finite and infinite critical points, judge the types of critical points with eigen-value, discuss all possible phrase portraits under the condition of parameter space according to equivariance and uniqueness and give their explicit form. There are five cases and sixteen phrase portraits.