Limit cycles for some families of smooth and non-smooth planar systems

We apply the averaging method in a class of planar systems given by a linear center perturbed by a sum of continuous homogeneous vector fields, to study lower bounds for their number of limit cycles. Our results can be applied to models where the smoothness is lost on the set Σ = {xy = 0}. They also...

Descripción completa

Detalles Bibliográficos
Autores: Buzzi, Claudio|||0000-0003-2037-8417, Carvalho, Yagor Romano|||0000-0001-7072-6016, Gasull, Armengol|||0000-0002-1719-8231
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:239781
Acceso en línea:https://ddd.uab.cat/record/239781
https://dx.doi.org/urn:doi:10.1016/j.na.2021.112298
Access Level:acceso abierto
Palabra clave:Limit cycles
First order averaging
Extended complete Chebyshev systems
Hilbert numbers
id ES_be62309ce82bc4c8b433a058eb1a2f21
oai_identifier_str oai:ddd.uab.cat:239781
network_acronym_str ES
network_name_str España
repository_id_str
spelling Limit cycles for some families of smooth and non-smooth planar systemsBuzzi, Claudio|||0000-0003-2037-8417Carvalho, Yagor Romano|||0000-0001-7072-6016Gasull, Armengol|||0000-0002-1719-8231Limit cyclesFirst order averagingExtended complete Chebyshev systemsHilbert numbersWe apply the averaging method in a class of planar systems given by a linear center perturbed by a sum of continuous homogeneous vector fields, to study lower bounds for their number of limit cycles. Our results can be applied to models where the smoothness is lost on the set Σ = {xy = 0}. They also motivate to consider a variant of Hilbert 16th problem, where the goal is to bound the number of limit cycles in terms of the number of monomials of a family of polynomial vector fields, instead of doing this in terms of their degrees. 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/239781https://dx.doi.org/urn:doi:10.1016/j.na.2021.112298reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617open 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:2397812026-06-06T12:50:31Z
dc.title.none.fl_str_mv Limit cycles for some families of smooth and non-smooth planar systems
title Limit cycles for some families of smooth and non-smooth planar systems
spellingShingle Limit cycles for some families of smooth and non-smooth planar systems
Buzzi, Claudio|||0000-0003-2037-8417
Limit cycles
First order averaging
Extended complete Chebyshev systems
Hilbert numbers
title_short Limit cycles for some families of smooth and non-smooth planar systems
title_full Limit cycles for some families of smooth and non-smooth planar systems
title_fullStr Limit cycles for some families of smooth and non-smooth planar systems
title_full_unstemmed Limit cycles for some families of smooth and non-smooth planar systems
title_sort Limit cycles for some families of smooth and non-smooth planar systems
dc.creator.none.fl_str_mv Buzzi, Claudio|||0000-0003-2037-8417
Carvalho, Yagor Romano|||0000-0001-7072-6016
Gasull, Armengol|||0000-0002-1719-8231
author Buzzi, Claudio|||0000-0003-2037-8417
author_facet Buzzi, Claudio|||0000-0003-2037-8417
Carvalho, Yagor Romano|||0000-0001-7072-6016
Gasull, Armengol|||0000-0002-1719-8231
author_role author
author2 Carvalho, Yagor Romano|||0000-0001-7072-6016
Gasull, Armengol|||0000-0002-1719-8231
author2_role author
author
dc.subject.none.fl_str_mv Limit cycles
First order averaging
Extended complete Chebyshev systems
Hilbert numbers
topic Limit cycles
First order averaging
Extended complete Chebyshev systems
Hilbert numbers
description We apply the averaging method in a class of planar systems given by a linear center perturbed by a sum of continuous homogeneous vector fields, to study lower bounds for their number of limit cycles. Our results can be applied to models where the smoothness is lost on the set Σ = {xy = 0}. They also motivate to consider a variant of Hilbert 16th problem, where the goal is to bound the number of limit cycles in terms of the number of monomials of a family of polynomial vector fields, instead of doing this in terms of their degrees.
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/239781
https://dx.doi.org/urn:doi:10.1016/j.na.2021.112298
url https://ddd.uab.cat/record/239781
https://dx.doi.org/urn:doi:10.1016/j.na.2021.112298
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
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617
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_ 1869418281258975232
score 15.300719

Similares en LA Referencia