Darboux theory of integrability in the sparse case

Autor:	Chèze, Guillaume
Rok vydání:	2012
Předmět:	Mathematics - Classical Analysis and ODEs Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
Popis:	Darboux's theorem and Jouanolou's theorem deal with the existence of first integrals and rational first integrals of a polynomial vector field. These results are given in terms of the degree of the polynomial vector field. Here we show that we can get the same kind of results if we consider the size of a Newton polytope associated to the vector field. Furthermore, we show that in this context the bound is optimal.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1210.7780 Zobrazit plný text záznamu View this record from Arxiv