幂零奇点小邻域内相轨线的拓扑结构与中心问题  

Topological structure and center problem in the neighborhood of a nilpotent singular point

作　　者：李锋 张冬梅 窦霁虹 Li Feng;Zhang Dongmei;Dou Jihong(School of Mathematics and statistics,Linyi University,Linyi 276005,China;School of Mathematics,Northwest University,Xi'an 710127,China)

机构地区：[1]临沂大学数学与统计学院,山东临沂276005 [2]西北大学数学学院,陕西西安710127

出　　处：《纯粹数学与应用数学》2022年第3期344-357,共14页Pure and Applied Mathematics

基　　金：国家自然科学基金(12071198)。

摘　　要：介绍幂零奇点小邻域内轨线的拓扑结构与中心问题的研究进展以及最近的一些结果.从三个方面来阐述这些结果:幂零奇点小邻域内相轨线的拓扑结构,幂零奇点的中心问题,幂零奇点的局部分支问题.也对幂零奇点的焦点量的计算方法进行了总结.In this paper,we introduce the recent results about topological structure and center problem in the neighborhood of a nilpotent singular point.It is divided into three sections,topological structure in the neighborhood of a nilpotent singular point,center and analytical center problem of a nilpotent singular point or degenerate singular point and bifurcation of limit cycles in the neighborhood of a nilpotent singular point.We also summarize some results about computation methods of focal values for nilpotent singular points.

关 键 词：椭圆扇区 双曲扇形 中心 解析中心 焦点量 极限环 

分 类 号：O175.12[理学—数学]