多项式微分系统的一类高次奇点的分析

On the Analysis of Higher Order Singular Points of Polynomial Differential Systems

分析多项式微分系统的奇点(0,0),当G(θ_0)=H(θ_0)=0时,沿其特征方向θ=θ_0有无轨线通向奇点(0,0)的问题,对于多项式微分系统简化了文献[4]的条件,从而便于直接应用,最后以例示之。

This paper deals with the higher order singular points of polynomial differential systems. We focus on the following problems: Are there any trajectories which have tangent line θ=θ0 and tend to the singular point of the system, when G(θ) = H(θ) = 0, where θ=θ0 is the characteristic direction of this singular point? The results for polynomial differential systems in this paper are one kind of simple forms of paper [4])'s, and hence the results of this paper are more convenient to use.