不变代数曲线与一类三次系统的中心判定问题  

INVARIANT ALGEBRAIC CURVES AND THE CENTER DETERMINATION PROBLEM FOR A CLASS OF CUBIC SYSTEMS

作　　者：桑波[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》2015年第5期611-616,共6页Journal of Systems Science and Mathematical Sciences

基　　金：数学天元基金(11226041);聊城大学实验技术研究基金(LDSY2014110)资助课题

摘　　要：对于一类具有一条抛物线解、两条直线解和中心-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它的第一阶焦点量为零.系统在原点的中心条件是通过不变代数曲线构造积分因子或利用Poincare对称原理得以证明.A class of cubic systems with a parabola, two straight lines and a center- focus type singular point, are proved to have a center at the origin if and only if the first focal value vanishes. The center conditions of the system at the origin are proved by constructing integrating factors formed from invariant algebraic curves or by the Poincaré symmetry principle.

关 键 词：三次微分系统 中心条件 积分因子 逆积分因子 极限环 

分 类 号：O186.11[理学—数学]