Analytic integrability of certain resonant saddle

We provide sufficient conditions of analytic integrability for a family of planar differential system with a p : −q resonant saddle at the origin. The conditions are then shown to be necessary in several finite dimensional families where the calculations can be performed explicitly. It is conjecture...

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Detalles Bibliográficos
Autores: Christopher, Colin, Giné, Jaume
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/72475
Acceso en línea:https://doi.org/10.1016/j.chaos.2021.110821
http://hdl.handle.net/10459.1/72475
Access Level:acceso abierto
Palabra clave:Blow-up
Resonant saddle
Saddle constants
Formal first integral
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spelling Analytic integrability of certain resonant saddleChristopher, ColinGiné, JaumeBlow-upResonant saddleSaddle constantsFormal first integralWe provide sufficient conditions of analytic integrability for a family of planar differential system with a p : −q resonant saddle at the origin. The conditions are then shown to be necessary in several finite dimensional families where the calculations can be performed explicitly. It is conjectured that the conditions are in fact complete for all families. Though the form of the equations is quite simple, their study merits further attention as they exhibit an interesting dichotomy between finite and arbitrary dimensional components of the center variety.The second author is partially supported by a MINECO/ FEDER grant number MTM2017-84383-P and an AGAUR (Generalitat de Catalunya) grant number 2017SGR-1276.Elsevier2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.1016/j.chaos.2021.110821http://hdl.handle.net/10459.1/72475reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)Inglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-84383-PReproducció del document publicat a https://doi.org/10.1016/j.chaos.2021.110821Chaos, Solitons & Fractals, 2021, vol. 146, 110821cc-by (c) Colin Christopher, Jaume Giné , 2021info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/oai:repositori.udl.cat:10459.1/724752026-06-24T12:42:17Z
dc.title.none.fl_str_mv Analytic integrability of certain resonant saddle
title Analytic integrability of certain resonant saddle
spellingShingle Analytic integrability of certain resonant saddle
Christopher, Colin
Blow-up
Resonant saddle
Saddle constants
Formal first integral
title_short Analytic integrability of certain resonant saddle
title_full Analytic integrability of certain resonant saddle
title_fullStr Analytic integrability of certain resonant saddle
title_full_unstemmed Analytic integrability of certain resonant saddle
title_sort Analytic integrability of certain resonant saddle
dc.creator.none.fl_str_mv Christopher, Colin
Giné, Jaume
author Christopher, Colin
author_facet Christopher, Colin
Giné, Jaume
author_role author
author2 Giné, Jaume
author2_role author
dc.subject.none.fl_str_mv Blow-up
Resonant saddle
Saddle constants
Formal first integral
topic Blow-up
Resonant saddle
Saddle constants
Formal first integral
description We provide sufficient conditions of analytic integrability for a family of planar differential system with a p : −q resonant saddle at the origin. The conditions are then shown to be necessary in several finite dimensional families where the calculations can be performed explicitly. It is conjectured that the conditions are in fact complete for all families. Though the form of the equations is quite simple, their study merits further attention as they exhibit an interesting dichotomy between finite and arbitrary dimensional components of the center variety.
publishDate 2021
dc.date.none.fl_str_mv 2021
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/10.1016/j.chaos.2021.110821
http://hdl.handle.net/10459.1/72475
url https://doi.org/10.1016/j.chaos.2021.110821
http://hdl.handle.net/10459.1/72475
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 2013-2016/MTM2017-84383-P
Reproducció del document publicat a https://doi.org/10.1016/j.chaos.2021.110821
Chaos, Solitons & Fractals, 2021, vol. 146, 110821
dc.rights.none.fl_str_mv cc-by (c) Colin Christopher, Jaume Giné , 2021
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
rights_invalid_str_mv cc-by (c) Colin Christopher, Jaume Giné , 2021
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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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