On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory

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Title:	On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory
Author:	Acosta-Humànez, Primitivo; Lázaro Ochoa, José Tomás; Morales Ruiz, Juan José; Pantazi, Chara
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC
Abstract:	We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Lienard equations and equations related with special functions such as Hypergeometric and Heun ones. The Poincare problem for some families is also approached.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -Algebra -Differential Galois theory -Darboux theory of integrability -Poincare problem -rational first integral -integrating factor -Riccati equation -Lienard equation -Liouvillian solution -invariant algebraic-curves -linear-differential equations -darboux integrating factors -inverse problems -1st integrals -poincare problem -galois theory -systems -foliations -multiplicity -Àlgebra diferencial
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Submitted version Article
Published by:	American Institute of Mathematical Sciences
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