具有抛物线解的一类三次系统的中心判定问题  

CENTER DETERMINATION PROBLEM FOR A CLASS OF CUBIC SYSTEMS WITH A PARABOLA SOLUTION

作　　者：桑波[1] 张兴秋[1] 

机构地区：[1]聊城大学数学科学学院,聊城252059

出　　处：《系统科学与数学》2013年第6期732-739,共8页Journal of Systems Science and Mathematical Sciences

基　　金：山东省优秀中青年科学家科研奖励基金(BS2010SF004)资助项目

摘　　要：对于一类具有抛物线解、直线解和中心-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 parobola, a straight line and a center-focus type singular point, are 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 factors formed from these 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：O174.14[理学—数学]