Monodromy and Dulac's problem for piecewise analytical planar vector fields

Autor(es)

Buzzi, Claudio A. ; Pessoa, Claudio ; Medrado, Joao C.

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN DES SCIENCES MATHEMATIQUES; v. 188, p. 27-pg., 2023-11-01.

Resumo

Consider an analytical function f : V subset of R-2 -> R having 0 as its regular value, a switching manifold Sigma = f(-1)(0) and a piecewise analytical vector field X = (X+, X-), i.e. X-+/- are analytical vector fields defined on Sigma(+/-) = {p is an element of V : +/- f (p) > 0}. We characterize when the vector field X has a monodromic singular point in Sigma, called Sigma-mono dromic singular point. Moreover, under certain conditions, we show that a Sigma-mono dromic singular point of X has a neighborhood free of limit cycles.(c) 2023 Elsevier Masson SAS. All rights reserved. (AU)

• Processo FAPESP: 18/19726-5 - Problema de Dulac e do Centro-Foco em Variedades Bidimensionais
• Beneficiário: Cláudio Gomes Pessoa
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático