一类多项式系统的中心条件

Conditions for a Center in a Simple Class of Cubic Systems

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.