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

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dc.contributor.authorBuzzi, Claudio A. [UNESP]
dc.contributor.authorRomano Carvalho, Yagor [UNESP]
dc.contributor.authorGasull, Armengol
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniv Autonoma Barcelona
dc.contributor.institutionCtr Recerca Matemat
dc.date.accessioned2021-06-25T12:41:41Z
dc.date.available2021-06-25T12:41:41Z
dc.date.issued2021-06-01
dc.description.abstractWe 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.en
dc.description.affiliationUniv Estadual Paulista, Math Dept, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil
dc.description.affiliationUniv Autonoma Barcelona, Dept Matemat, Edif Cc, E-08193 Barcelona, Spain
dc.description.affiliationCtr Recerca Matemat, Edif Cc,Campus Bellaterra, Barcelona 08193, Spain
dc.description.affiliationUnespUniv Estadual Paulista, Math Dept, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil
dc.description.sponsorshipMinisterio de Ciencia e Innovacion, Spain
dc.description.sponsorshipAgencia de Gestio d'Ajuts Universitaris i de Recerca, Spain
dc.description.sponsorshipCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipIdMinisterio de Ciencia e Innovacion, Spain: PID2019-104658GBI00
dc.description.sponsorshipIdAgencia de Gestio d'Ajuts Universitaris i de Recerca, Spain: 2017 SGR 1617
dc.description.sponsorshipIdCAPES: 88881.068462/2014-01
dc.description.sponsorshipIdCNPq: 304798/2019-3
dc.description.sponsorshipIdFAPESP: 2019/10269-3
dc.description.sponsorshipIdFAPESP: 2018/05098-2
dc.description.sponsorshipIdFAPESP: 2016/00242-2
dc.format.extent13
dc.identifierhttp://dx.doi.org/10.1016/j.na.2021.112298
dc.identifier.citationNonlinear Analysis-theory Methods & Applications. Oxford: Pergamon-elsevier Science Ltd, v. 207, 13 p., 2021.
dc.identifier.doi10.1016/j.na.2021.112298
dc.identifier.issn0362-546X
dc.identifier.lattes6682867760717445
dc.identifier.orcid0000-0003-2037-8417
dc.identifier.urihttp://hdl.handle.net/11449/210166
dc.identifier.wosWOS:000634580300011
dc.language.isoeng
dc.publisherElsevier B.V.
dc.relation.ispartofNonlinear Analysis-theory Methods & Applications
dc.sourceWeb of Science
dc.subjectLimit cycles
dc.subjectFirst order averaging
dc.subjectExtended complete Chebyshev systems
dc.subjectHilbert numbers
dc.titleLimit cycles for some families of smooth and non-smooth planar systemsen
dc.typeArtigo
dcterms.licensehttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dcterms.rightsHolderElsevier B.V.
unesp.author.lattes6682867760717445[1]
unesp.author.orcid0000-0003-2037-8417[1]

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