Bounding the number of remarkable values via Jouanolou's theorem
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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Classical Analysis and ODEs
Dynamical Systems
Exactly Solvable and Integrable Systems
