关于平面多项式微分系统的代数不变式曲线
On the algebraic invariant curves of plane polynomial differential systems
摘要：
本文考虑一个平面多项式向量场$P(x,y)dx+Q(x,y)dy$，其次数为$m>1$ .对于这样一个域的每一条代数不变式曲线，我们用亚纯微分$ω=dx/P=dy/Q$来表示紧致黎曼曲面。本文给出了任意代数不变式曲线阶的渐近估计，在光滑情况下，D. Cerveau和A. Lins Neto [Ann. Inst. Fourier Grenoble 41，883-903]以不同的方式。
英文摘要：
We consider a plane polynomial vector field $P(x,y)dx+Q(x,y)dy$ of degree $m>1$. To each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential $ω=dx/P=dy/Q$. The asymptotic estimate of the degree of an arbitrary algebraic invariant curve is found. In the smooth case this estimate was already found by D. Cerveau and A. Lins Neto [Ann. Inst. Fourier Grenoble 41, 883-903] in a different way.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
