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arXiv · 1310.1275

Bounding the number of remarkable values via Jouanolou's theorem

Guillaume Chèze
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Abstract

In this article we bound the number of remarkable values of a polynomial vector field. The proof is short and based on Jouanolou's theorem about rational first integrals of planar polynomial derivations. Our bound is given in term of the size of a Newton polygon associated to the vector field. We prove that this bound is almost reached.

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BibTeXRIS

Guillaume Chèze. 2013-10-04. Bounding the number of remarkable values via Jouanolou's theorem. https://doi.org/10.1016/j.jde.2015.01.027

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