一类可逆四次微分系统的细中心(英文)

Weak Centers of a Cubic Isochrone Perturbed by Fourth Degree Homogeneous Polynomial

讨论了一类相应三次系统具有等时中心的可逆四次多项式微分系统的细中心.应用多项式结式计算方法确定了本四次系统的细中心阶数,并给出其具有等时中心的条件.

The authors discussed a reversible polynomial differential system of fourth degree, which is a system of cubic isochrone perturbed by fourth degree homogeneous polynomial. By computing resultants of polynomials, orders of weak centers are detremined. Moreover, conditions for the system to have an isochrone at the origin are given.