A sufficient condition in order that the real Jacobian conjecture in R-2 holds

Autor(es)

Braun, Francisco ^[1] ; Gine, Jaume ^[2] ; Llibre, Jaume ^[3]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Paulo - Brazil

^[2] Univ Lleida, Dept Matemat, Lleida, Catalonia - Spain

^[3] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Catalonia - Spain

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 260, n. 6, p. 5250-5258, MAR 15 2016.
• Citações Web of Science: 2

Resumo

Let F = (f,g):R-2 -> R-2 be a polynomial map such that detDF(x, y) is different from zero for all (x, y) epsilon R-2 and F(0, 0) = (0, 0). We prove that for the injectivity of F it is sufficient to assume that the higher homogeneous terms of the polynomials ff(x) + gg(x) and ff(y) + gg(y) do not have real linear factors in common. The proofs are based on qualitative theory of dynamical systems. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 14/26149-3 - Injetividade de aplicações polinomiais no plano
• Beneficiário: Francisco Braun
• Modalidade de apoio: Bolsas no Exterior - Pesquisa