Periods of solutions of periodic differential equations

Smooth non-autonomous T-periodic differential equations x'(t)=f(t,x(t)) defined in \R\K^n, where \K is \R or \C and n 2 can have periodic solutions with any arbitrary period~S. We show that this is not the case when n=1. We prove that in the real C^1-setting the period of a non-constant periodi...

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Autores: Cimà, Anna|||0000-0003-0256-518X, Gasull, Armengol|||0000-0002-1719-8231, Mañosas, Francesc|||0000-0003-2535-0501
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169473
Acceso en línea:https://ddd.uab.cat/record/169473
Access Level:acceso abierto
Palabra clave:Holomorphic differential equations
Periodic differential equations
Periodic orbit
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spelling Periods of solutions of periodic differential equationsCimà, Anna|||0000-0003-0256-518XGasull, Armengol|||0000-0002-1719-8231Mañosas, Francesc|||0000-0003-2535-0501Holomorphic differential equationsPeriodic differential equationsPeriodic orbitSmooth non-autonomous T-periodic differential equations x'(t)=f(t,x(t)) defined in \R\K^n, where \K is \R or \C and n 2 can have periodic solutions with any arbitrary period~S. We show that this is not the case when n=1. We prove that in the real C^1-setting the period of a non-constant periodic solution of the scalar differential equation is a divisor of the period of the equation, that is T/S\N. Moreover, we characterize the structure of the set of the periods of all the periodic solutions of a given equation. We also prove similar results in the one-dimensional holomorphic setting. In this situation the period of any non-constant periodic solution is commensurable with the period of the equation, that is T/S\Q. 22016-01-0120162016-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/169473reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-859Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40998-PMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-52209-C2-1-Popen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1694732026-06-06T12:50:31Z
dc.title.none.fl_str_mv Periods of solutions of periodic differential equations
title Periods of solutions of periodic differential equations
spellingShingle Periods of solutions of periodic differential equations
Cimà, Anna|||0000-0003-0256-518X
Holomorphic differential equations
Periodic differential equations
Periodic orbit
title_short Periods of solutions of periodic differential equations
title_full Periods of solutions of periodic differential equations
title_fullStr Periods of solutions of periodic differential equations
title_full_unstemmed Periods of solutions of periodic differential equations
title_sort Periods of solutions of periodic differential equations
dc.creator.none.fl_str_mv Cimà, Anna|||0000-0003-0256-518X
Gasull, Armengol|||0000-0002-1719-8231
Mañosas, Francesc|||0000-0003-2535-0501
author Cimà, Anna|||0000-0003-0256-518X
author_facet Cimà, Anna|||0000-0003-0256-518X
Gasull, Armengol|||0000-0002-1719-8231
Mañosas, Francesc|||0000-0003-2535-0501
author_role author
author2 Gasull, Armengol|||0000-0002-1719-8231
Mañosas, Francesc|||0000-0003-2535-0501
author2_role author
author
dc.subject.none.fl_str_mv Holomorphic differential equations
Periodic differential equations
Periodic orbit
topic Holomorphic differential equations
Periodic differential equations
Periodic orbit
description Smooth non-autonomous T-periodic differential equations x'(t)=f(t,x(t)) defined in \R\K^n, where \K is \R or \C and n 2 can have periodic solutions with any arbitrary period~S. We show that this is not the case when n=1. We prove that in the real C^1-setting the period of a non-constant periodic solution of the scalar differential equation is a divisor of the period of the equation, that is T/S\N. Moreover, we characterize the structure of the set of the periods of all the periodic solutions of a given equation. We also prove similar results in the one-dimensional holomorphic setting. In this situation the period of any non-constant periodic solution is commensurable with the period of the equation, that is T/S\Q.
publishDate 2016
dc.date.none.fl_str_mv 2
2016-01-01
2016
2016-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/169473
url https://ddd.uab.cat/record/169473
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-568
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-859
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40998-P
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-52209-C2-1-P
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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