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

dc.contributor.authorAcosta-Humànez, Primitivo
dc.contributor.authorLázaro Ochoa, José Tomás
dc.contributor.authorMorales Ruiz, Juan José
dc.contributor.authorPantazi, Chara
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2019-02-27T06:43:29Z
dc.date.available2019-02-27T06:43:29Z
dc.date.issued2015-05-01
dc.identifier.citationAcosta-Humànez, P. [et al.]. On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory. "Discrete and continuous dynamical systems. Series A", 1 Maig 2015, vol. 35, núm. 5, p. 1767-1800.
dc.identifier.issn1078-0947
dc.identifier.urihttp://hdl.handle.net/2117/129783
dc.description.abstractWe 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.
dc.format.extent34 p.
dc.language.isoeng
dc.publisherAmerican Institute of Mathematical Sciences
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshAlgebra
dc.subject.otherDifferential Galois theory
dc.subject.otherDarboux theory of integrability
dc.subject.otherPoincare problem
dc.subject.otherrational first integral
dc.subject.otherintegrating factor
dc.subject.otherRiccati equation
dc.subject.otherLienard equation
dc.subject.otherLiouvillian solution
dc.subject.otherinvariant algebraic-curves
dc.subject.otherlinear-differential equations
dc.subject.otherdarboux integrating factors
dc.subject.otherinverse problems
dc.subject.other1st integrals
dc.subject.otherpoincare problem
dc.subject.othergalois theory
dc.subject.othersystems
dc.subject.otherfoliations
dc.subject.othermultiplicity
dc.titleOn the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory
dc.typeArticle
dc.subject.lemacÀlgebra diferencial
dc.contributor.groupUniversitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC
dc.identifier.doi10.3934/dcds.2015.35.1767
dc.relation.publisherversionhttp://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10632
dc.rights.accessOpen Access
local.identifier.drac15389009
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO/PE/MTM-31714
local.citation.authorAcosta-Humànez, P.; Lazaro, J. Tomás; Morales, J.; Pantazi, C.
local.citation.publicationNameDiscrete and continuous dynamical systems. Series A
local.citation.volume35
local.citation.number5
local.citation.startingPage1767
local.citation.endingPage1800


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