New lower bounds of the number of critical periods in reversible centers

In this paper we aim to find the highest number of critical periods in a class of planar systems of polynomial differential equations for fixed degree having a center. We fix our attention to lower bounds of local criticality for low degree planar polynomial centers. The main technique is the study...

Descripción completa

Detalles Bibliográficos
Autores: Sanchez Sanchez, Ivan|||0000-0002-4534-3870, Torregrosa, Joan|||0000-0002-2753-1827
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:257085
Acceso en línea:https://ddd.uab.cat/record/257085
https://dx.doi.org/urn:doi:10.1016/j.jde.2021.05.013
Access Level:acceso abierto
Palabra clave:Bifurcation of critical periods
Criticality
Period constants
Period function
Time-reversible centers
id ES_f1eec6be690ec08d3f179d0bb8aa81f7
oai_identifier_str oai:ddd.uab.cat:257085
network_acronym_str ES
network_name_str España
repository_id_str
spelling New lower bounds of the number of critical periods in reversible centersSanchez Sanchez, Ivan|||0000-0002-4534-3870Torregrosa, Joan|||0000-0002-2753-1827Bifurcation of critical periodsCriticalityPeriod constantsPeriod functionTime-reversible centersIn this paper we aim to find the highest number of critical periods in a class of planar systems of polynomial differential equations for fixed degree having a center. We fix our attention to lower bounds of local criticality for low degree planar polynomial centers. The main technique is the study of perturbations of reversible holomorphic (isochronous) centers, inside the reversible centers class. More concretely, we study the Taylor developments of the period constants with respect to the perturbation parameters. First, we see that there are systems of degree 3≤n≤16 for which up to first order at least (n+n-4)/2 critical periods bifurcate from the center. Second, we improve this number for centers with degree from 3 to 9. In particular, we obtain 6 and 10 critical periods for cubic and quartic degree systems, respectively. 22021-01-0120212021-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/257085https://dx.doi.org/urn:doi:10.1016/j.jde.2021.05.013reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00Ministerio de Educación, Cultura y Deporte https://doi.org/10.13039/501100003176 FPU16/04317Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617European Commission https://doi.org/10.13039/501100000780 777911open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2570852026-06-06T12:50:31Z
dc.title.none.fl_str_mv New lower bounds of the number of critical periods in reversible centers
title New lower bounds of the number of critical periods in reversible centers
spellingShingle New lower bounds of the number of critical periods in reversible centers
Sanchez Sanchez, Ivan|||0000-0002-4534-3870
Bifurcation of critical periods
Criticality
Period constants
Period function
Time-reversible centers
title_short New lower bounds of the number of critical periods in reversible centers
title_full New lower bounds of the number of critical periods in reversible centers
title_fullStr New lower bounds of the number of critical periods in reversible centers
title_full_unstemmed New lower bounds of the number of critical periods in reversible centers
title_sort New lower bounds of the number of critical periods in reversible centers
dc.creator.none.fl_str_mv Sanchez Sanchez, Ivan|||0000-0002-4534-3870
Torregrosa, Joan|||0000-0002-2753-1827
author Sanchez Sanchez, Ivan|||0000-0002-4534-3870
author_facet Sanchez Sanchez, Ivan|||0000-0002-4534-3870
Torregrosa, Joan|||0000-0002-2753-1827
author_role author
author2 Torregrosa, Joan|||0000-0002-2753-1827
author2_role author
dc.subject.none.fl_str_mv Bifurcation of critical periods
Criticality
Period constants
Period function
Time-reversible centers
topic Bifurcation of critical periods
Criticality
Period constants
Period function
Time-reversible centers
description In this paper we aim to find the highest number of critical periods in a class of planar systems of polynomial differential equations for fixed degree having a center. We fix our attention to lower bounds of local criticality for low degree planar polynomial centers. The main technique is the study of perturbations of reversible holomorphic (isochronous) centers, inside the reversible centers class. More concretely, we study the Taylor developments of the period constants with respect to the perturbation parameters. First, we see that there are systems of degree 3≤n≤16 for which up to first order at least (n+n-4)/2 critical periods bifurcate from the center. Second, we improve this number for centers with degree from 3 to 9. In particular, we obtain 6 and 10 critical periods for cubic and quartic degree systems, respectively.
publishDate 2021
dc.date.none.fl_str_mv 2
2021-01-01
2021
2021-01-01
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/257085
https://dx.doi.org/urn:doi:10.1016/j.jde.2021.05.013
url https://ddd.uab.cat/record/257085
https://dx.doi.org/urn:doi:10.1016/j.jde.2021.05.013
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 PID2019-104658GB-I00
Ministerio de Educación, Cultura y Deporte https://doi.org/10.13039/501100003176 FPU16/04317
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617
European Commission https://doi.org/10.13039/501100000780 777911
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
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://creativecommons.org/licenses/by-nc-nd/4.0/
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869424230115835904
score 15,301603

Similares en LA Referencia