Algebraic invariant curves of plane polynomial differential systems
نویسنده
چکیده
We consider a plane polynomial vector field P(x, y) dx +Q(x, y) dy of degree m > 1. With 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 has already been found by Cerveau and Lins Neto in a different way. AMS classification scheme number: 34C07
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