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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 Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -Differential equations, Linear -Galois theory -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 -Galois, Teoria de -Equacions diferencials lineals -Classificació AMS::12 Field theory and polynomials::12H Differential and difference algebra -Classificació AMS::32 Several complex variables and analytic spaces::32S Singularities
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Published version Article
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