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dc.contributor.authorLázaro Ochoa, José Tomás
dc.contributor.authorPantazi, Chara
dc.contributor.authorAcosta Humanez, Primitivo
dc.contributor.authorMorales Ruiz, Juan José
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationLazaro, 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.description.abstractWe 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.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshDifferential algebra
dc.subject.lcshGalois theory
dc.titleDifferential galois theory and non-integrability of planar polynomial vector fields
dc.subject.lemacÀlgebra diferencial
dc.subject.lemacGalois, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC
dc.description.peerreviewedPeer Reviewed
dc.rights.accessRestricted access - publisher's policy
dc.description.versionPostprint (author's final draft)
local.citation.authorLazaro, J. Tomás; Pantazi, C.; Acosta, P.; Morales, J.
local.citation.publicationNameJournal of differential equations

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