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

All of RECERCAT

To access the full text documents, please follow this link: http://hdl.handle.net/2117/14764

Title:	On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory
Author:	Lázaro Ochoa, José Tomás; Morales Ruíz, Juan José; Acosta Humánez, Primitivo Belén; 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, Li\'enard equations and equations related with special functions such as Hypergeometric and Heun ones. We also study the Poincar\'e problem for some of the families.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -Galois theory -Differential equations, Linear -Camps vectorials -Galois, Teoria de -Equacions diferencials lineals
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Draft Report
Share: