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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Braun, Francisco [1] ; Gine, Jaume [2] ; Llibre, Jaume [3]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: Journal of Differential Equations; v. 260, n. 6, p. 5250-5258, MAR 15 2016.
Web of Science Citations: 2
Abstract

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)

FAPESP's process: 14/26149-3 - Injectivity of polynomial maps in the plane
Grantee:Francisco Braun
Support Opportunities: Scholarships abroad - Research