Bounding the number of remarkable values via Jouanolou's theorem

12 Feb 2015  ·  Chèze Guillaume IMT ·

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. read more

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Classical Analysis and ODEs Dynamical Systems Exactly Solvable and Integrable Systems