Inverse Jacobi multipliers and first integrals for nonautonomous differential systems

dc.contributor.authorBuica, Adriana
dc.contributor.authorGarcía, I. A. (Isaac A.)
dc.date.accessioned2016-11-02T12:04:29Z
dc.date.available2016-11-02T12:04:29Z
dc.date.issued2015-05-01
dc.date.updated2016-11-02T12:04:30Z
dc.description.abstractIn this paper we consider nonautonomous differential systems of arbitrary dimension and first find expressions for their inverse Jacobi multipliers and first integrals in some nonautonomous invariant set in terms of the solutions of the differential system. Given an inverse Jacobi multiplier $V$, we find a relation between the Poincar\'{e} translation map $\Pi$ at time $T$ that extends to arbitrary dimensions the fundamental relation for scalar equations, $V(T,\Pi(x))=V(0,x)\Pi'(x)$, found in Trans. Amer. Math. Soc. 362 (2010), 3591-3612. The main result guarantees the existence of continua of $T$-periodic solutions for $T$-periodic systems in the presence of $T$-periodic first integrals and inverse Jacobi multipliers.
dc.description.sponsorshipThe authors are partially supported by a MCYT/FEDER grant number MTM2008-00694 and by a CIRIT grant number 2014 SGR 1204.
dc.format.mimetypeapplication/pdf
dc.identifier.doihttps://doi.org/10.1007/s00033-014-0440-7
dc.identifier.idgrec022983
dc.identifier.issn0044-2275
dc.identifier.urihttp://hdl.handle.net/10459.1/58351
dc.language.isoeng
dc.publisherSpringer Basel
dc.relationinfo:eu-repo/grantAgreement/MICINN//MTM2008-00694/ES/METODOS CUALITATIVOS E INTEGRABILIDAD EN LAS ECUACIONES DIFERENCIALES EN EL PLANO/
dc.relation.isformatofVersió postprint del document publicat a https://doi.org/10.1007/s00033-014-0440-7
dc.relation.ispartofZeitschrift für Angewandte Mathematik und Physik, 2015, vol. 66, p. 573-585
dc.rights(c)Springer Basel, 2015
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.subjectNon-autonomous systems
dc.subjectInverse Jacobi multipliers
dc.titleInverse Jacobi multipliers and first integrals for nonautonomous differential systems
dc.typeinfo:eu-repo/semantics/article
dc.type.versionacceptedVersion
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