【摘要】 当中心邻域的闭轨周期为常数时,该中心称为等时中心.解决等时中心问题的主要难点在于周期系数代数簇的分解和横截交换系统的计算.对于一类含有三次非线性项的时间可逆四次系统,给出了周期系数的递推算法,在此基础上,利用吴方法得到了系统具有等时中心的充要条件.更多还原

【Abstract】 A center is called an isochronous center if those periodic orbits in some neighbourhood of it have the same period.The main difficulty in proving isochronicity is algebraic variety decompositions for period coefficients and finding transversal commuting systems.For a class of time-reversible quartic system with third order terms,a recursive algorithm for computing period coefficients is given,with which necessary and sufficient conditions for isochronicity are obtained by Wu Wen-tsun method.更多还原