平面曲线局部性质的数值化与极限环

Numerization to Local Property of Plane Curve and Limit Cycles

本文通过引入非对称度、拱度、偏度等概念,刻画平面曲线的局部性质,获得平面曲线局部性质的数值化理论,并应用此数值化理论讨论平面微分系统极限环的求解问题,为极限环的研究,特别是希尔伯特第16个问题有关极限环的存在个数问题的研究,提供一种新的研究思路与方法。

In this paper, we characterize the local properties of plane curves by introducing the geometric concepts of asymmetry, archness and skewness, and obtain the local numerical theory of plane curves. We discuss the solving process of limit cycles by numerization to local property of plane curve, which is the study of limit cycles. A new idea and method are given for study to limit cycles, especially the existence of limit cycles in Hilbert’s 16th problem.