一类二阶微分系统在无穷远处奇点的稳定性

从系统(1)右端多项式的系数中构造一个矩阵A，由矩阵A的特征根，特征向量来直接确定系统(1)的奇点类型及其稳定性。依文献【2】知，A有三个互异的特征根λi(I=123)且分别对应三个线性无关的特征向量：依文献【1】知A有两个互异的特征根且对应两个线性无关的特征向量.本文对上述两种情况进行了讨论，并论证了雅可比型系统在无穷远处的奇点不能运用文献【1】、【2】的方法去判断奇点的稳定性。此类奇点应该把文献【1】、【2】、【3】结合起来去判断系统(1)在无穷远处的奇点稳定性。

Research on stability of odd points of special second differential system

In the paper we have constructed a matrx A from multionomial confficients of the system (1) on the rithe. Thus the kinds and stability of odd points are directly determined by characteristic roots characteristic vectors. Kinds and stability of odd points are directly determined by characteristic roots and characteristic vectors. This paper discusses the above two problem, and proves Jacobi type system at special odd points can not use the method in literature 1],2], determinating stability of odd points. This type odd points can be combined with literature1],2],3] determinating special odd points of the system (1).