【摘要】 为了以解析的方法和代数的方法寻求二阶多项式自治系统的代数曲线解，并为进一步研究非线性系统的可积性和复域上多项式系统的定性理论，证明了关于复域上二元多项式的一个整除定理，并以ＶａｎｄｅｒＰｏｌ方程及一个二阶二次自治系统为例，说明这一整除定理可以作为二阶多项式自治系统是否存在代数曲线解的主要判据．更多还原

【Abstract】 For the sake of finding the algebraic curve solution to the second order polynomial autonomous system by the methods of analysis and algebra,moreover,in order to further discuss the integrability of the nonlinear system and the qualitative theory of the polynomial system in the complex domain,a division theorem of the polynomial functions of two variables in the complex domain is proved,with the Van der Pci equation and a second order quadratic polynomial system as concrete examples,it is shown that the division theorem can be used for the judement on the existence of algebraic ctirve solution to the second order polynomial autonomous system.更多还原