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Entree


Nilpotent centers from analytical systems on center manifolds

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Autor(es):
Pessoa, Claudio ; Queiroz, Lucas
Número total de Autores: 2
Tipo de documento: Artigo Científico
Fonte: Journal of Mathematical Analysis and Applications; v. 525, n. 1, p. 17-pg., 2023-03-02.
Resumo

Consider analytical three-dimensional differential systems having a singular point at the origin such that its linear part is y partial derivative(chi) - lambda z partial derivative(z) for some lambda not equal 0. The restriction of such systems to a Center Manifold has a nilpotent singular point at the origin. We prove that if the restricted system is analytic and has a nilpotent center at the origin, with Andreev number 2, then the three-dimensional system admits a formal inverse Jacobi multiplier. We also prove that nilpotent centers of three-dimensional systems, on analytic center manifolds, are limits of Hopf-type centers. We use these results to solve the center problem for some three-dimensional systems without restricting the system to a parametrization of the center manifold. (AU)

Processo FAPESP: 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II
Beneficiário:Claudio Aguinaldo Buzzi
Modalidade de apoio: Auxílio à Pesquisa - Temático
Processo FAPESP: 19/13040-7 - Centros nilpotentes sobre variedades centrais
Beneficiário:Lucas Queiroz Arakaki
Modalidade de apoio: Bolsas no Brasil - Doutorado