一类多项式系统的中心条件  

Conditions for a Center in a Simple Class of Cubic Systems

作　　者：诸慧[1] Zhu Hui(Wenzhou Vocational College of Science and Technology,Department of Public Education,Wenzhou 325000,China)

机构地区：[1]温州科技职业学院公共教学部,浙江温州325000

出　　处：《科学技术创新》2022年第16期45-48,共4页Scientific and Technological Innovation

摘　　要：本文考虑如下微分方程系统dx/dt=-y+x(a_(1)x+a_(2)x^(2)+·+a_(n)x^(n)),dy/dt=x+y(b_(1)y+b_(2)y^(2)+·+b_(n)y^(n))这,里ai,bi是实数,根据Poincare对称原理和结式消元,利用计算机软件Maple辅助证明,得到了当n=4,5,6,7时,原点为系统中心的充要条件。In this paper,the following differential dynamical systems with degree n are considered dx/dt=-y+x(a_(1)x+a_(2)x^(2)+·+a_(n)x^(n)),dy/dt=x+y(b_(1)y+b_(2)y^(2)+·+b_(n)y^(n))where ai,bi are real number,according to Poincare symmetry principle and resultant elimination,it is proved with the aid of computer software maple,the sufficient and essential condition for the origin to be a center of the system are obtained for n=4,5,6,7.

关 键 词：中心 焦点量 结式 对称性 

分 类 号：O175.13[理学—数学]