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

被引：13

作者：

Braun, Francisco ^{[1
]}

Gine, Jaume ^{[2
]}

Llibre, Jaume ^{[3
]}

机构：

[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

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 260卷 / 06期

基金：

巴西圣保罗研究基金会;

关键词：

Real Jacobian conjecture; Global injectivity; Centre; INJECTIVITY;

D O I：

10.1016/j.jde.2015.12.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：5250 / 5258

页数：9

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