一类退化奇点的极限环分支  

Bifurcation of limit cycles for a class of degenerate singular point

作　　者：张齐[1] 邹序焱[1] 

机构地区：[1]中南大学数学科学与计算技术学院,长沙410075

出　　处：《华中师范大学学报（自然科学版）》2008年第2期159-162,共4页Journal of Central China Normal University：Natural Sciences

基　　金：湖南省自然科学基金资助项目(06JJ200006);中南大学博士后基金资助项目.

摘　　要：研究了一类有一个小参数和六个普通参数的五次系统的退化奇点的极限环分支.用一同胚变换将退化奇点转变成初等奇点进而计算了原点的Lyapunov常数(奇点量),并由此得到了原点的中心条件.通过参数的微小扰动,给出了一个在原点有7个极限环的五次多项式系统的实例.This paper studied bifurcation of limit cycles at the degenerate singular point in a class of quintic system with one small parameter and six normal parameters. The method is based on a homeomorphic transformation of the degenerate singular point into elementary singular point, which allows us to compute the generalized Lyapunov constants （the singular point quantities）for the origin and derive the center conditions for the degenerate singular point. Under small perturbation of parameters, a quintic system with 7 limit cycles bifurcating from the origin is constructed.

关 键 词：退化奇点 五次多项式系统 同胚变换 中心条件 极限环分支 

分 类 号：O175.12[理学—数学]