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

Detalhes bibliográficos
Autor(a) principal: Buzzi, Claudio A. [UNESP]
Data de Publicação: 2021
Outros Autores: Romano Carvalho, Yagor [UNESP], Gasull, Armengol
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.na.2021.112298
http://hdl.handle.net/11449/210166
Resumo: 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 Sigma = {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. (C) 2021 Elsevier Ltd. All rights reserved.
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spelling Limit cycles for some families of smooth and non-smooth planar systemsLimit 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 Sigma = {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. (C) 2021 Elsevier Ltd. All rights reserved.Ministerio de Ciencia e Innovacion, SpainAgencia de Gestio d'Ajuts Universitaris i de Recerca, SpainCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Univ Estadual Paulista, Math Dept, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilUniv Autonoma Barcelona, Dept Matemat, Edif Cc, E-08193 Barcelona, SpainCtr Recerca Matemat, Edif Cc,Campus Bellaterra, Barcelona 08193, SpainUniv Estadual Paulista, Math Dept, BR-15054000 Sao Jose Do Rio Preto, SP, BrazilMinisterio de Ciencia e Innovacion, Spain: PID2019-104658GBI00Agencia de Gestio d'Ajuts Universitaris i de Recerca, Spain: 2017 SGR 1617CAPES: 88881.068462/2014-01CNPq: 304798/2019-3FAPESP: 2019/10269-3FAPESP: 2018/05098-2FAPESP: 2016/00242-2Elsevier B.V.Universidade Estadual Paulista (Unesp)Univ Autonoma BarcelonaCtr Recerca MatematBuzzi, Claudio A. [UNESP]Romano Carvalho, Yagor [UNESP]Gasull, Armengol2021-06-25T12:41:41Z2021-06-25T12:41:41Z2021-06-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article13http://dx.doi.org/10.1016/j.na.2021.112298Nonlinear Analysis-theory Methods & Applications. Oxford: Pergamon-elsevier Science Ltd, v. 207, 13 p., 2021.0362-546Xhttp://hdl.handle.net/11449/21016610.1016/j.na.2021.112298WOS:00063458030001166828677607174450000-0003-2037-8417Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNonlinear Analysis-theory Methods & Applicationsinfo:eu-repo/semantics/openAccess2021-12-10T14:36:49Zoai:repositorio.unesp.br:11449/210166Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-12-10T14:36:49Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
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 A. [UNESP]
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
author Buzzi, Claudio A. [UNESP]
author_facet Buzzi, Claudio A. [UNESP]
Romano Carvalho, Yagor [UNESP]
Gasull, Armengol
author_role author
author2 Romano Carvalho, Yagor [UNESP]
Gasull, Armengol
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Univ Autonoma Barcelona
Ctr Recerca Matemat
dc.contributor.author.fl_str_mv Buzzi, Claudio A. [UNESP]
Romano Carvalho, Yagor [UNESP]
Gasull, Armengol
dc.subject.por.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 Sigma = {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. (C) 2021 Elsevier Ltd. All rights reserved.
publishDate 2021
dc.date.none.fl_str_mv 2021-06-25T12:41:41Z
2021-06-25T12:41:41Z
2021-06-01
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1016/j.na.2021.112298
Nonlinear Analysis-theory Methods & Applications. Oxford: Pergamon-elsevier Science Ltd, v. 207, 13 p., 2021.
0362-546X
http://hdl.handle.net/11449/210166
10.1016/j.na.2021.112298
WOS:000634580300011
6682867760717445
0000-0003-2037-8417
url http://dx.doi.org/10.1016/j.na.2021.112298
http://hdl.handle.net/11449/210166
identifier_str_mv Nonlinear Analysis-theory Methods & Applications. Oxford: Pergamon-elsevier Science Ltd, v. 207, 13 p., 2021.
0362-546X
10.1016/j.na.2021.112298
WOS:000634580300011
6682867760717445
0000-0003-2037-8417
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Nonlinear Analysis-theory Methods & Applications
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 13
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv Web of Science
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1803649409772158976

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