多项式微分系统的等价性

Equivalence of the polynomial differential systems

应用反射函数建立了多项式微分方程=Pn(t,x)与其扰动方程=Pn(t,x)+α(t)Δ(t,x)之间的等价关系,并给出了当Δ(t,x)=Qn(t,x)时,它们之间等价的充分条件.该结论推广了周正新等关于Abel方程研究的相关结论.

We use the reflective function to construct the equivalence between the polynomial differential system x=Pn（t,x） and its perturbed differential systems x=Pn（t,x）＋α（t）Δ（t,x）.Particularly,for Δ（t,x）=Qn（t,x）,we obtain a set of sufficient conditions for the equivalence.The conclusion generalizes the research done by Zhou Zhengxin on the Abel equation.