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dc.rights.licenseLicencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacionalspa
dc.contributor.authorAcosta-Humánez, Primitivo B.
dc.contributor.authorLázaro, J. Tomás
dc.contributor.authorMorales-Ruiz, Juan J.
dc.contributor.authorPantazi, Chara
dc.date.accessioned2018-05-08T14:40:28Z
dc.date.available2018-05-08T14:40:28Z
dc.date.issued2018-06
dc.identifier.issn00220396
dc.identifier.urihttp://hdl.handle.net/20.500.12442/2087
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 integrabilitywith some higher transcendent functions, like the error function.eng
dc.language.isoengspa
dc.publisherElsevierspa
dc.rightsinfo:eu-repo/semantics/openAccess
dc.sourceJournal of Differential Equationseng
dc.sourceVol. 264, No.12 (2018)spa
dc.source.urihttps://reader.elsevier.com/reader/sd/9AC79E5FF1C81427C9C71E1D6F14CCC5D4BC562F3248DB8006AD5A72DEFA8259852833B9E4CBD7D2BCB88DC7F6706567eng
dc.titleDifferential Galois theory and non-integrability of planar polynomial vector fieldsspa
dc.typearticlespa
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