Bounding the number of remarkable values via Jouanolou's theorem
Classical Analysis and ODEs
2015-02-13 v2 Dynamical Systems
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.1310.1275,
title = {Bounding the number of remarkable values via Jouanolou's theorem},
author = {Guillaume Chèze},
journal= {arXiv preprint arXiv:1310.1275},
year = {2015}
}