平面二次向量场多项式首次积分的不存在性

摘要

考虑平面二次向量场多项式首次积分的不存在性. 通过把多项式系统看作负半拟齐次系统, 利用Kowalevskaya指数, 给出了一般平面二次系统存在非平凡多项式首次积分的一些充分条件.%The authors considered the nonexistence of polynomial first integrals for quadratic planar vector fields, which can be treated as negative semi-homogeneous systems. Using the Kowalevskaya exponents, we gave some simple criteria for the nonexistence of nontrivial polynomial first integrals for planar vector fields.