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On plane polynomial vector fields and the Poincaré problem

open access: yesElectronic Journal of Differential Equations, 2002
Summary: We address the Poincaré problem, on plane polynomial vector fields, under some conditions on the nature of the singularities of invariant curves. Our main idea consists in transforming a given vector field of degree \(m\) into another one of degree at most \(m+1\) having its invariant curves in projective quasi-generic position. This allows us
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