定性理论中的奇点分类及其拓扑等价性

TAXONOMY AND TOPOLOGY EQUIVALENCE OF ODD NUMBER IN QUALITATIVE THEORY

对于平面自治系统,本文从线性系统入手分析其轨线在相平面上的性态,研究其奇点邻域内的轨线分布,根据分布的不同情况归纳出九种不同类型的奇点,并且在此基础上讨论一般自治系统与其相应的标准系统之间在齐次线性变换下的拓扑等价性。

On plane self - control system, the author analyzes the character of locus on the parallel side from linear character system, He researches the distribution of locus in the scope of the odd number, and summarizes nine kinds of odd numbers according to different distributions and he discusses the topology equivalence character between general self- control system and its relevant standard systems on the basis.