具有一对共轭复不变直线的三次系统的中心判定问题  

Center Determination Problem for a Class of Cubic System with a Pair of Invariant Conjugate Imaginary Straight Lines

作　　者：桑波[1] 

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《南京师大学报（自然科学版）》2013年第1期16-21,共6页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：数学天元基金项目(11226041)

摘　　要：对于一类具有一对共轭复不变直线和中心-焦点型奇点的三次系统,证明它以原点为中心的充要条件是其前五阶焦点量全为零.此中心条件是通过不变代数曲线构造积分因子或对称原理得以证明.A class of cubic systems with a pair of invariant conjugate imaginary straight lines and a center-focus type singular point, is proved to have a center at the origin if and only if the first five focal values vanish. The presence of a center at the origin is proved by constructing integrating factor formed from invariant algebraic curves or by symmetry principle.

关 键 词：三次微分系统 中心条件 积分因子 对称原理 

分 类 号：O175.12[理学—数学]