【摘要】 通过将多项式系统看作负半拟齐次系统,利用它的Kowalevsky指数,给出了多项式系统存在有理首次积分的必要条件,即给出了一个判别多项式系统有理不可积性的简单准则.更多还原

【Abstract】 Taking the polynomial system as a semi-quasihomogeneous one,and using the so called Kowalevsky exponents,we gave a necessary condition for polynomial systems to have rational first integral.In fact,the result obtained in this paper has provided a simple criterion of nonintegrability for polynomial systems.更多还原