Sobre a geometria Lipschitz de polinômios quase-homogeneos

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dc.contributor.advisor1Câmara, Leonardo Meireles
dc.contributor.advisor1IDhttps://orcid.org/0000-0002-4637-8573
dc.contributor.advisor1Latteshttp://lattes.cnpq.br/9240898305551070
dc.contributor.authorAquino Neto, Gabriel da Macena de
dc.contributor.authorIDhttps://orcid.org/0009-0002-3889-6044
dc.contributor.authorLatteshttp://lattes.cnpq.br/0868237399371299
dc.contributor.referee1Silva, Thiago Filipe da
dc.contributor.referee1IDhttps://orcid.org/0000-0002-3152-0987
dc.contributor.referee1Latteshttp://lattes.cnpq.br/5049713215002090
dc.contributor.referee2Fernandes, Alexandre César Gurgel
dc.contributor.referee2IDhttps://orcid.org/0000-0001-7846-0312
dc.contributor.referee2Latteshttp://lattes.cnpq.br/8791056897839415
dc.date.accessioned2025-03-26T23:04:02Z
dc.date.available2025-03-26T23:04:02Z
dc.date.issued2024-10-21
dc.description.abstractIn this work, we will show how to determine, in a general context, whether two real quasi-homogeneous polynomials in two variables with weights ϖ = (p,q) are R-semialgebraically Lipschitz equivalent. Initially, we characterize the Lipschitz equivalence of real polynomial functions of one variable by comparing the values and also the multiplicities of the polynomial functions at their critical points. Sub sequently, under general conditions, we will reduce the problem of R-semialgebraic Lipschitz equivalence of quasi-homogeneous polynomials in two variables to the pro blem of Lipschitz equivalence of real polynomial functions of one variable. As an application of the theory developed throughout this dissertation, we will analyze the properties, in the context of R-semialgebraic Lipschitz equivalence, of a specific fa mily of quasi-homogeneous polynomials considered in [9, Henry and Parusinski], to show that the bi-Lipschitz equivalence of germs of analytic functions (R2,0) → (R,0) admits continuous moduli. Consequently, the R-semialgebraic Lipschitz equivalence of real quasi-homogeneous polynomials in two variables also admits continuous mo duli. Finally, we explore the possibility of simplifying the classification space of quasi-homogeneous polynomials.
dc.description.sponsorshipFundação de Amparo à Pesquisa e Inovação do Espírito Santo (FAPES)
dc.formatText
dc.identifier.urihttp://repositorio.ufes.br/handle/10/18831
dc.languagepor
dc.language.isopt
dc.publisherUniversidade Federal do Espírito Santo
dc.publisher.countryBR
dc.publisher.courseMestrado em Matemática
dc.publisher.departmentCentro de Ciências Exatas
dc.publisher.initialsUFES
dc.publisher.programPrograma de Pós-Graduação em Matemática
dc.rightsopen access
dc.rights.urihttps://creativecommons.org/licenses/by-nc-sa/4.0/
dc.subjectR-equivalência Lipschitz semi-algébrica
dc.subjectPolinômios quase-homogêneos
dc.subjectModuli contínuo
dc.subjectR-semialgebraic Lipschitz equivalence
dc.subjectQuasihomogeneous polynomials
dc.subjectContinuous moduli
dc.subject.cnpqÁrea(s) do conhecimento do documento (Tabela CNPq)
dc.titleSobre a geometria Lipschitz de polinômios quase-homogeneos
dc.typemasterThesis
foaf.mboxemail@ufes.br
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