一次线性奇点附近轨线拓扑结构的若干问题

On Some Problems about Linear Odd-point Nearby Locus Topological Structures

关于一次线性奇点附近轨线拓扑结构,理论分析工作是完整的,但对具体的作出轨线图的详细过程一般教科书和参考书中没有仔细的讨论,特别是轨线图和过渡矩阵P没有给出具体的求法或者求法太难。本文主要解决了变换矩阵的具体求法以及变换后坐标系的确定问题,以便能对给定的一次线性微分方程组尽快画出轨线图,比较直观的了解奇点附近轨线的拓扑结构。

The theory of linear odd-point nearby locus topological structure was completed,but the processing about making the locus picture in the references has not been introduced in details yet. This paper points out that the methods of locuspictureand alternate matrix Pare very difficult to learn; thereforethespecific method ofalternatematrix and howto get the coordinate system after alternate matrix isintroduced in this paper.