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On the algebraic invariant curves of plane polynomial differential systems

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Published in Journal of Physics. A, Mathematical and General. 2001, vol. 34, no. 3, p. 663-672
Abstract 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 $omega=dx/P=dy/Q$. 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.
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Deposited on : 2010-11-08

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