A sufficient condition in order that the real Jacobian conjecture in R2 holds

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Braun, Francisco¹  Gine, Jaume²  Llibre, Jaume³ 

[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

关键词: Real Jacobian conjecture;    Global injectivity;    Centre;   

DOI  :  10.1016/j.jde.2015.12.011

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free