二次系统奇点的分支问题

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Bifurcation Problem of Critical Points for Quadratic Differential Systems

Department of Mathematics, Nanjing Normal University, Nanjing 210024, P. R. China

摘要: 本水文研究了(Ⅱ)和(Ⅲ)类的二次系统奇点的分支,并回答了[1]中提出的问题.
- 二次系统 /
- 发散量 /
- 奇点
Abstract: In this paper foe bifurcation of critical points for the quadratic systems of type (Ⅱ) and (Ⅲ) is investigated. and an answer to the problem given in [1] is given.
- quadratic system /
- divergence /
- critical point

[1]	Ye Yanqian.Qualitative theory of the quadratic differential systems (I) Chin,Ann.Math (to appear).
[2]	Ye Yanqian,Limit cycles and bifurcation phenomena for the quardatic differentialsystem (Ⅲ)m=0 having three anti-saddle (I) Chin Ann Math 17B.2 (1996),167-174.
[3]	A.Zegeling,Separatrix cycles and multiple limit cycles in a class of quadratic systems.J Diff.Eqs.113,2 (1994),355-380.
[4]	F.Dumortier,R.Roussarie and C.Rousseau,Hilbert's 16th problem for quadraticvector fields,J.Diff.Eqs. 110,1 (1994),86-133.
[5]	Ye Yanqian et al.Theory of limit cycles,Trans.Math.Monographs,Amer.Math Soc.66 (1986).
[6]	Ye Yanqian,Qualilative Theory' of Polynomial Differential Systems, Shanghai Science Technical Publisher,Shanghai (1995).
[7]	J.W.Reyn and R.E.Kooij,Infinite singular points of quadratic systems in the plane,Nonlinear Analysis.Theorey,Methods & Applications.24,6 (1995),895-927.