Inverse Jacobi multipliers and first integrals for nonautonomous differential systems

In 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...

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Autores: Buica, Adriana, García, I. A. (Isaac A.)
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2015
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/58351
Acceso en línea:https://doi.org/10.1007/s00033-014-0440-7
http://hdl.handle.net/10459.1/58351
Access Level:acceso abierto
Palabra clave:Non-autonomous systems
Inverse Jacobi multipliers
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spelling Inverse Jacobi multipliers and first integrals for nonautonomous differential systemsBuica, AdrianaGarcía, I. A. (Isaac A.)Non-autonomous systemsInverse Jacobi multipliersIn 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.The authors are partially supported by a MCYT/FEDER grant number MTM2008-00694 and by a CIRIT grant number 2014 SGR 1204.Springer Basel2015info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://doi.org/10.1007/s00033-014-0440-7http://hdl.handle.net/10459.1/58351reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)Inglésinfo:eu-repo/grantAgreement/MICINN//MTM2008-00694Versió postprint del document publicat a https://doi.org/10.1007/s00033-014-0440-7Zeitschrift für Angewandte Mathematik und Physik, 2015, vol. 66, p. 573-585(c)Springer Basel, 2015info:eu-repo/semantics/openAccessoai:repositori.udl.cat:10459.1/583512026-06-24T12:42:17Z
dc.title.none.fl_str_mv Inverse Jacobi multipliers and first integrals for nonautonomous differential systems
title Inverse Jacobi multipliers and first integrals for nonautonomous differential systems
spellingShingle Inverse Jacobi multipliers and first integrals for nonautonomous differential systems
Buica, Adriana
Non-autonomous systems
Inverse Jacobi multipliers
title_short Inverse Jacobi multipliers and first integrals for nonautonomous differential systems
title_full Inverse Jacobi multipliers and first integrals for nonautonomous differential systems
title_fullStr Inverse Jacobi multipliers and first integrals for nonautonomous differential systems
title_full_unstemmed Inverse Jacobi multipliers and first integrals for nonautonomous differential systems
title_sort Inverse Jacobi multipliers and first integrals for nonautonomous differential systems
dc.creator.none.fl_str_mv Buica, Adriana
García, I. A. (Isaac A.)
author Buica, Adriana
author_facet Buica, Adriana
García, I. A. (Isaac A.)
author_role author
author2 García, I. A. (Isaac A.)
author2_role author
dc.subject.none.fl_str_mv Non-autonomous systems
Inverse Jacobi multipliers
topic Non-autonomous systems
Inverse Jacobi multipliers
description In 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.
publishDate 2015
dc.date.none.fl_str_mv 2015
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1007/s00033-014-0440-7
http://hdl.handle.net/10459.1/58351
url https://doi.org/10.1007/s00033-014-0440-7
http://hdl.handle.net/10459.1/58351
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MICINN//MTM2008-00694
Versió postprint del document publicat a https://doi.org/10.1007/s00033-014-0440-7
Zeitschrift für Angewandte Mathematik und Physik, 2015, vol. 66, p. 573-585
dc.rights.none.fl_str_mv (c)Springer Basel, 2015
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c)Springer Basel, 2015
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Basel
publisher.none.fl_str_mv Springer Basel
dc.source.none.fl_str_mv reponame:Repositori Obert UdL
instname:Universitat de Lleida (UdL)
instname_str Universitat de Lleida (UdL)
reponame_str Repositori Obert UdL
collection Repositori Obert UdL
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