On Periodic Orbits of Vector Fields in Arbitrary Dimension Via Autonomous and Nonautonomous Inverse Jacobi Multipliers

We investigate periodic orbits of C1 autonomous vector fields in Rn using inverse Jacobi multipliers that may depend explicitly on time. We establish a localization principle for T -periodic orbits in arbitrary dimension, extending known planar results and deriving nonexistence conditions through th...

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Autores: García, I. A. (Isaac A.), Latorre, Ernest, Maza Sabido, Susanna
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2026
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:dnet:.___________::54dcfb4e5517823266db7e0b790beb4e
Acceso en línea:https://doi.org/10.1007/s12346-026-01490-4
https://hdl.handle.net/10459.1/469955
Access Level:acceso abierto
Palabra clave:Vector fields
Inverse Jacobi multipliers
Periodic orbits
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spelling On Periodic Orbits of Vector Fields in Arbitrary Dimension Via Autonomous and Nonautonomous Inverse Jacobi MultipliersGarcía, I. A. (Isaac A.)Latorre, ErnestMaza Sabido, SusannaVector fieldsInverse Jacobi multipliersPeriodic orbitsWe investigate periodic orbits of C1 autonomous vector fields in Rn using inverse Jacobi multipliers that may depend explicitly on time. We establish a localization principle for T -periodic orbits in arbitrary dimension, extending known planar results and deriving nonexistence conditions through the relation between the time-slices V(0, ·) and V(T , ·). We further characterize hyperbolicity and orbital stability, including a decomposition of characteristic multipliers along invariant surfaces associated with autonomous inverse Jacobi multipliers. A test for the algebraicity of periodic orbits in 3-dimensional vector fields is given based on non-autonomous inverse Jacobi multipliers. The interplay between normalizers, inverse Jacobi multipliers and invariants is analyzed, with applications to the Lorenz and Rössler systems.The authors are partially supported by the Agencia Estatal de Investigación grant PID2020-113758GB-I00 and an AGAUR (Generalitat de Catalunya) grant number 2021SGR 01618.Springer2026info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.1007/s12346-026-01490-4https://hdl.handle.net/10459.1/469955reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)Inglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113758GB-I00Reproducció del document publicat a https://doi.org/10.1007/s12346-026-01490-4Qualitative Theory of Dynamical Systems, 2026, vol. 25, 68cc-by (c) Isaac A. García, Ernest Latorre, Susanna Maza, 2026Attribution 4.0 Internationalinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/oai:dnet:.___________::54dcfb4e5517823266db7e0b790beb4e2026-06-24T12:42:17Z
dc.title.none.fl_str_mv On Periodic Orbits of Vector Fields in Arbitrary Dimension Via Autonomous and Nonautonomous Inverse Jacobi Multipliers
title On Periodic Orbits of Vector Fields in Arbitrary Dimension Via Autonomous and Nonautonomous Inverse Jacobi Multipliers
spellingShingle On Periodic Orbits of Vector Fields in Arbitrary Dimension Via Autonomous and Nonautonomous Inverse Jacobi Multipliers
García, I. A. (Isaac A.)
Vector fields
Inverse Jacobi multipliers
Periodic orbits
title_short On Periodic Orbits of Vector Fields in Arbitrary Dimension Via Autonomous and Nonautonomous Inverse Jacobi Multipliers
title_full On Periodic Orbits of Vector Fields in Arbitrary Dimension Via Autonomous and Nonautonomous Inverse Jacobi Multipliers
title_fullStr On Periodic Orbits of Vector Fields in Arbitrary Dimension Via Autonomous and Nonautonomous Inverse Jacobi Multipliers
title_full_unstemmed On Periodic Orbits of Vector Fields in Arbitrary Dimension Via Autonomous and Nonautonomous Inverse Jacobi Multipliers
title_sort On Periodic Orbits of Vector Fields in Arbitrary Dimension Via Autonomous and Nonautonomous Inverse Jacobi Multipliers
dc.creator.none.fl_str_mv García, I. A. (Isaac A.)
Latorre, Ernest
Maza Sabido, Susanna
author García, I. A. (Isaac A.)
author_facet García, I. A. (Isaac A.)
Latorre, Ernest
Maza Sabido, Susanna
author_role author
author2 Latorre, Ernest
Maza Sabido, Susanna
author2_role author
author
dc.subject.none.fl_str_mv Vector fields
Inverse Jacobi multipliers
Periodic orbits
topic Vector fields
Inverse Jacobi multipliers
Periodic orbits
description We investigate periodic orbits of C1 autonomous vector fields in Rn using inverse Jacobi multipliers that may depend explicitly on time. We establish a localization principle for T -periodic orbits in arbitrary dimension, extending known planar results and deriving nonexistence conditions through the relation between the time-slices V(0, ·) and V(T , ·). We further characterize hyperbolicity and orbital stability, including a decomposition of characteristic multipliers along invariant surfaces associated with autonomous inverse Jacobi multipliers. A test for the algebraicity of periodic orbits in 3-dimensional vector fields is given based on non-autonomous inverse Jacobi multipliers. The interplay between normalizers, inverse Jacobi multipliers and invariants is analyzed, with applications to the Lorenz and Rössler systems.
publishDate 2026
dc.date.none.fl_str_mv 2026
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1007/s12346-026-01490-4
https://hdl.handle.net/10459.1/469955
url https://doi.org/10.1007/s12346-026-01490-4
https://hdl.handle.net/10459.1/469955
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113758GB-I00
Reproducció del document publicat a https://doi.org/10.1007/s12346-026-01490-4
Qualitative Theory of Dynamical Systems, 2026, vol. 25, 68
dc.rights.none.fl_str_mv cc-by (c) Isaac A. García, Ernest Latorre, Susanna Maza, 2026
Attribution 4.0 International
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
rights_invalid_str_mv cc-by (c) Isaac A. García, Ernest Latorre, Susanna Maza, 2026
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
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