一类扰动系统的弱Hilbert第16问题  

ABOUT A WEAKENED HILBERT 16-TH PROBLEM OF A CLASS OF PERTURBED SYSTEMS

作　　者：王锋[1] 

机构地区：[1]江汉大学数学及计算机系,武汉430019

出　　处：《数学杂志》2002年第2期221-225,共5页Journal of Mathematics

摘　　要：动Hamilten系统 ,给出了当其一阶Melnikov函数恒等于零时的二阶Melnikov函数的表达式 ,并由此研究了由该系统的Poincare分支及Hopf分支产生的极限环数目 ,得到了当二阶Melnikov函数不恒为零时 ,该系统的极限环个数的最小上界的完整结论 .In this paper, about the Melnikov' function for a class perturbed system are discussed, we get an expression of M 2(h) of this system when M 1(h)≡0, and the number of limit cycles produced by Poincare bifurcation and Hopf bifurcation are study, For this system, if M 1(h)≡0 and M 2r(h)≡0, we get an integrated conclusion of the least upper-bound of the number of limit cycles of this system.

关 键 词：扰动系数 MELNIKOV函数 POINCARE分支 HOPF分支 

分 类 号：O177.91[理学—数学]