The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5

The interest in studying the uniform isochronous centers goes back to C. Huygens in the XVII century. Since then, many papers have been published on this subject. In particular, the phase portraits of the polynomial uniform isochronous center up to degree four have been classified. In this paper, we...

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Autores: Dong, Guangfeng, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:318292
Acceso en línea:https://ddd.uab.cat/record/318292
https://dx.doi.org/urn:doi:10.1007/s10883-025-09734-3
Access Level:acceso embargado
Palabra clave:Uniform isochronous center
Polynomial vector field
Phase portrait
Separatrix configuration
Periodic orbit
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spelling The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5Dong, GuangfengLlibre, Jaume|||0000-0002-9511-5999Uniform isochronous centerPolynomial vector fieldPhase portraitSeparatrix configurationPeriodic orbitThe interest in studying the uniform isochronous centers goes back to C. Huygens in the XVII century. Since then, many papers have been published on this subject. In particular, the phase portraits of the polynomial uniform isochronous center up to degree four have been classified. In this paper, we classify the topological phase portraits of polynomial differential systems with a uniform isochronous center, whose nonlinear part is a homogeneous polynomial of degree 5. We prove that there are three distinct topological phase portraits in the Poincaré disc for such polynomial differential systems. 220252025-01-0120262026-06-30Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articlehttps://ddd.uab.cat/record/318292https://dx.doi.org/urn:doi:10.1007/s10883-025-09734-3reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2022-136613NB-100European Commission https://doi.org/10.13039/501100000780 777911Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2021/SGR-00113embargoed accesshttp://purl.org/coar/access_right/c_f1cfAquest 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/embargoedAccessoai:ddd.uab.cat:3182922026-06-06T12:50:31Z
dc.title.none.fl_str_mv The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5
title The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5
spellingShingle The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5
Dong, Guangfeng
Uniform isochronous center
Polynomial vector field
Phase portrait
Separatrix configuration
Periodic orbit
title_short The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5
title_full The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5
title_fullStr The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5
title_full_unstemmed The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5
title_sort The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5
dc.creator.none.fl_str_mv Dong, Guangfeng
Llibre, Jaume|||0000-0002-9511-5999
author Dong, Guangfeng
author_facet Dong, Guangfeng
Llibre, Jaume|||0000-0002-9511-5999
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
author2_role author
dc.subject.none.fl_str_mv Uniform isochronous center
Polynomial vector field
Phase portrait
Separatrix configuration
Periodic orbit
topic Uniform isochronous center
Polynomial vector field
Phase portrait
Separatrix configuration
Periodic orbit
description The interest in studying the uniform isochronous centers goes back to C. Huygens in the XVII century. Since then, many papers have been published on this subject. In particular, the phase portraits of the polynomial uniform isochronous center up to degree four have been classified. In this paper, we classify the topological phase portraits of polynomial differential systems with a uniform isochronous center, whose nonlinear part is a homogeneous polynomial of degree 5. We prove that there are three distinct topological phase portraits in the Poincaré disc for such polynomial differential systems.
publishDate 2025
dc.date.none.fl_str_mv
2
2025
2025-01-01
2026
2026-06-30
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/318292
https://dx.doi.org/urn:doi:10.1007/s10883-025-09734-3
url https://ddd.uab.cat/record/318292
https://dx.doi.org/urn:doi:10.1007/s10883-025-09734-3
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2022-136613NB-100
European Commission https://doi.org/10.13039/501100000780 777911
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2021/SGR-00113
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dc.rights.openaire.fl_str_mv info:eu-repo/semantics/embargoedAccess
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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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