37 research outputs found
On the algebraic invariant curves of plane polynomial differential systems
We consider a plane polynomial vector field of degree
. To each algebraic invariant curve of such a field we associate a compact
Riemann surface with the meromorphic differential . 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.Comment: 10 pages, Latex, to appear in J.Phys.A:Math.Ge