On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory
Acosta-Humánez, Primitivo B. (Universidad del Atlántico and Intelectual.Co. Department of Mathematics (Colombia))
Lázaro, J. Tomás (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
Morales Ruiz, Juan J. (Universidad Politécnica de Madrid. Departamento de Matemática Aplicada)
Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)

Date:	2015
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, Liénard equations and equations related with special functions such as Hypergeometric and Heun ones. The Poincaré problem for some families is also approached.
Grants:	Ministerio de Ciencia e Innovación MTM2009-06973 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-859 Ministerio de Ciencia e Innovación MTM2008-03437
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Differential Galois Theory ; Darboux theory of Integrability ; Poincaré problem ; Rational first integral ; Integrating factor ; Riccati equation ; Liénard Equation ; Liouvillian solution
Published in:	Discrete and continuous dynamical systems. Series A, Vol. 35, Issue 5 (May 2015) , p. 1767-1800, ISSN 1553-5231

DOI: 10.3934/dcds.2015.35.1767

Postprint 32 p, 490.7 KB

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