Injetividade de aplicações polinomiais via resolubilidade de campos vetoriais

• Autor(a) principal: Braun, Francisco
• Data de Publicação: 2010
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/5816
• topic: Análise matemática; Campos vetoriais; Campos hamiltonianos; Topologia; Geometria; Injetividade; Mathematical analysis; Vector fields; Injectivity; CIENCIAS EXATAS E DA TERRA::MATEMATICA

Let F : Rn → Rn be a polynomial map such that the derivative map DF(x) be invertible for each x ∈ Rn. In this work, using techniques of solvability of suitable vector fields, we investigate the role of the degree of F in its injectivity. In R2, we show that if the degree of one of the components of F is less or equal 3, then F is injective. In Rn, we discuss the injectivity of the maps F(x) = x + H(x), where H : Rn → Rn is a homogeneous polinomial map of degree 3 and detDF(x) = 1, ∀x ∈ Rn. Here we propose a new way to approach this problem. We show the injectivity when n = 3.