一类三次多项式微分系统的周期解

On Periodic Solutions of a Class of Cubic Polynomial Differential System

根据Mironenko的反射函数理论,给出一种利用多项式方程探讨三次多项式微分系统周期解的几何性质的新方法.该文首先研究一类系统具有满足特定关系式的反射函数的结构,由此建立三次多项式微分系统与多项式方程之间的解的对应关系,然后利用此对应关系探讨三次多项式微分系统的周期解的几何性质.

According to Mironenko＇s method about how to apply the polynom class of cubic polynomial differential sys when it satisfies the special relations and ship between a class of cubic polynomial reflective function theory, ial equations discussing the tern. We di we use the differential this paper gives a new qualitative behavior of a scuss the structure of reflective function reflective function to establish a relationsystem and the polynomial differential equations. The obtained conclusions are used to discussing the qualitative behavior of solutions of above cubic polynomial differential system.