Bounding the number of remarkable values via Jouanolou's theorem

Autor:	Chèze, Guillaume
Rok vydání:	2013
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Dynamical Systems Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jde.2015.01.027
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1310.1275 Zobrazit plný text záznamu View this record from Arxiv