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

Francisco Braun; Jaume Giné; Jaume Llibre

doi:https://doi.org/10.1016/j.jde.2015.12.011

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

Francisco Braun, Jaume Giné, Jaume Llibre

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

6 Citations (Scopus)

Abstract

© 2015 Elsevier Inc. Let F=(f,g):R2 → R2 be a polynomial map such that det DF(x, y) is different from zero for all (x,y) ∈ R2 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 ffx+ggx and ffy+ggy do not have real linear factors in common. The proofs are based on qualitative theory of dynamical systems.

Original language	English
Pages (from-to)	5250-5258
Journal	Journal of Differential Equations
Volume	260
Issue number	6
DOIs	https://doi.org/10.1016/j.jde.2015.12.011
Publication status	Published - 15 Mar 2016

Keywords

Centre
Global injectivity
Real Jacobian conjecture

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https://doi.org/10.1016/j.jde.2015.12.011

https://ddd.uab.cat/record/169471

Cite this

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abstract = "{\textcopyright} 2015 Elsevier Inc. Let F=(f,g):R2 → R2 be a polynomial map such that det DF(x, y) is different from zero for all (x,y) ∈ R2 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 ffx+ggx and ffy+ggy do not have real linear factors in common. The proofs are based on qualitative theory of dynamical systems.",

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AU - Braun, Francisco

AU - Giné, Jaume

AU - Llibre, Jaume

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N2 - © 2015 Elsevier Inc. Let F=(f,g):R2 → R2 be a polynomial map such that det DF(x, y) is different from zero for all (x,y) ∈ R2 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 ffx+ggx and ffy+ggy do not have real linear factors in common. The proofs are based on qualitative theory of dynamical systems.

AB - © 2015 Elsevier Inc. Let F=(f,g):R2 → R2 be a polynomial map such that det DF(x, y) is different from zero for all (x,y) ∈ R2 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 ffx+ggx and ffy+ggy do not have real linear factors in common. The proofs are based on qualitative theory of dynamical systems.

KW - Centre

KW - Global injectivity

KW - Real Jacobian conjecture

U2 - https://doi.org/10.1016/j.jde.2015.12.011

DO - https://doi.org/10.1016/j.jde.2015.12.011

M3 - Article

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SP - 5250

EP - 5258

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

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