Tesis
Injetividade de aplicações polinomiais via resolubilidade de campos vetoriais
Fecha
2010-08-19Registro en:
BRAUN, Francisco. Injetividade de aplicações polinomiais via resolubilidade de campos vetoriais. 2010. 61 f. Tese (Doutorado em Ciências Exatas e da Terra) - Universidade Federal de São Carlos, São Carlos, 2010.
Autor
Braun, Francisco
Institución
Resumen
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.