摘要
Hilbert第16问题的第二部分是,对于方程 (其中P_n(x,y)与Q_n(x,y)是x和y的n次互项多项式),在相平面上至多有几个极限环,其相对位置如何?这个问题提出至今已有85年,但要彻底解决尚有不小距离.本文不可能对这个问题的进展作全面的介绍,仅对n=2即二次系统自八十年代以来的工作,就本人所知,作一综述.文中也有若干是我们第一次发表的结果.国内许多同行,为本文提供资料并提出宝贵意见,作者在此深表威谢.
The second part of Hiblert's 16-th problem is to determine the maximum number of limit cycles and their relative positions for the planar autonomous differential systemsdx/dt=Pn(x,y), dy/dt = Qn(x,y),where Pn and Qn are polynomials of degree n. This paper surveys the recent advance in the study of quadratic differential systems (i. e. the case n = 2) . Some new results are given as well. The survey consists of four sections. ?1 Separatrix cycles and Dulac's Theorem. ? On the study of Ye Yanqian's classification. ? Focal values, saddle values and the number of the limit cycles. ?4 Some specific quadratic differential systems.
出处
《数学进展》
CSCD
北大核心
1989年第1期5-21,共17页
Advances in Mathematics（China）
基金
国家教委科技基金资助
