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

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

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor	Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.contributor.author	Lázaro Ochoa, José Tomás
dc.contributor.author	Morales Ruíz, Juan José
dc.contributor.author	Acosta Humánez, Primitivo Belén
dc.contributor.author	Pantazi, Chara
dc.date	2012-01-12
dc.identifier.citation	Lázaro, J. [et al.]. "On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory". 2012.
dc.identifier.uri	http://hdl.handle.net/2117/14764
dc.language.iso	eng
dc.relation	http://arxiv.org/abs/1012.4796v2
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject	Galois theory
dc.subject	Differential equations, Linear
dc.subject	Camps vectorials
dc.subject	Galois, Teoria de
dc.subject	Equacions diferencials lineals
dc.title	On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory
dc.type	info:eu-repo/semantics/draft
dc.type	info:eu-repo/semantics/report
dc.description.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.

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