dc.contributor.author Lázaro Ochoa, José Tomás dc.contributor.author Pantazi, Chara dc.contributor.author Acosta Humanez, Primitivo dc.contributor.author Morales Ruiz, Juan José dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2018-03-14T12:06:15Z dc.date.issued 2018-02-26 dc.identifier.citation Lazaro, J. Tomás, Pantazi, C., Acosta, P., Morales, J. Differential galois theory and non-integrability of planar polynomial vector fields. "Journal of differential equations", 26 Febrer 2018, vol. 264, núm. 12, p.7183-7212 dc.identifier.issn 0022-0396 dc.identifier.uri http://hdl.handle.net/2117/115168 dc.description.abstract We study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular solution it is obtained a necessary condition for the existence of a rational first integral. The method is systematic starting with the first order variational equation. We illustrate this result with several families of examples. A key point is to check whether a suitable primitive is elementary or not. Using a theorem by Liouville, the problem is equivalent to the existence of a rational solution of a certain first order linear equation, the Risch equation. This is a classical problem studied by Risch in 1969, and the solution is given by the “Risch algorithm”. In this way we point out the connection of the non integrability with some higher transcendent functions, like the error function dc.language.iso eng dc.rights Attribution-NonCommercial-NoDerivs 3.0 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística dc.subject.lcsh Differential algebra dc.subject.lcsh Galois theory dc.title Differential galois theory and non-integrability of planar polynomial vector fields dc.type Article dc.subject.lemac Àlgebra diferencial dc.subject.lemac Galois, Teoria de dc.contributor.group Universitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC dc.identifier.doi 10.1016/j.jde.2018.02.016 dc.description.peerreviewed Peer Reviewed dc.relation.publisherversion https://www.sciencedirect.com/science/article/pii/S0022039618300998 dc.rights.access Restricted access - publisher's policy local.identifier.drac 22001005 dc.description.version Postprint (author's final draft) dc.date.lift 10000-01-01 local.citation.author Lazaro, J. Tomás; Pantazi, C.; Acosta, P.; Morales, J. local.citation.publicationName Journal of differential equations
﻿