The local period function for Hamiltonian systems with applications

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dc.contributor.authorBuzzi, Claudio A. [UNESP]
dc.contributor.authorCarvalho, Yagor Romano [UNESP]
dc.contributor.authorGasull, Armengol
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniv Autonoma Barcelona
dc.contributor.institutionCtr Recerca Matemat
dc.date.accessioned2021-06-25T12:38:21Z
dc.date.available2021-06-25T12:38:21Z
dc.date.issued2021-04-15
dc.description.abstractIn the first part of the paper we develop a constructive procedure to obtain the Taylor expansion, in terms of the energy, of the period function for a non-degenerated center of any planar analytic Hamiltonian system. We apply it to several examples, including the whirling pendulum and a cubic Hamiltonian system. The knowledge of this Taylor expansion of the period function for this system is one of the key points to study the number of zeroes of an Abelian integral that controls the number of limit cycles bifurcating from the periodic orbits of a planar Hamiltonian system that is inspired by a physical model on capillarity. Several other classical tools, like for instance Chebyshev systems are applied to study this number of zeroes. The approach introduced can also be applied in other situations. (C) 2021 Elsevier Inc. 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, Cerdanyola Del Valles 08193, Barcelona, Spain
dc.description.affiliationCtr Recerca Matemat, Edif Cc,Campus Bellaterra, Cerdanyola Del Valles 08193, Barcelona, Spain
dc.description.affiliationUnespUniv Estadual Paulista, Math Dept, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil
dc.description.sponsorshipMinisterio de Ciencia e Innovacion
dc.description.sponsorshipAgencia de Gestio d'Ajuts Universitaris i de Recerca
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: PID2019-104658GB-I00
dc.description.sponsorshipIdAgencia de Gestio d'Ajuts Universitaris i de Recerca: 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.extent590-617
dc.identifierhttp://dx.doi.org/10.1016/j.jde.2021.01.033
dc.identifier.citationJournal Of Differential Equations. San Diego: Academic Press Inc Elsevier Science, v. 280, p. 590-617, 2021.
dc.identifier.doi10.1016/j.jde.2021.01.033
dc.identifier.issn0022-0396
dc.identifier.lattes6682867760717445
dc.identifier.orcid0000-0003-2037-8417
dc.identifier.urihttp://hdl.handle.net/11449/210058
dc.identifier.wosWOS:000620331000019
dc.language.isoeng
dc.publisherElsevier B.V.
dc.relation.ispartofJournal Of Differential Equations
dc.sourceWeb of Science
dc.subjectPeriod function
dc.subjectLimit cycles
dc.subjectAbelian integrals
dc.subjectExtended complete Chebyshev systems
dc.subjectPicard-Fuchs differential equations
dc.titleThe local period function for Hamiltonian systems with applicationsen
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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