Sobre a geometria Lipschitz de polinômios quase-homogeneos
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Data
2024-10-21
Autores
Aquino Neto, Gabriel da Macena de
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Universidade Federal do Espírito Santo
Resumo
In 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.
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R-equivalência Lipschitz semi-algébrica , Polinômios quase-homogêneos , Moduli contínuo , R-semialgebraic Lipschitz equivalence , Quasihomogeneous polynomials , Continuous moduli