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

Francisco Braun, Jaume Giné, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

5 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 languageEnglish
Pages (from-to)5250-5258
JournalJournal of Differential Equations
Volume260
Issue number6
DOIs
Publication statusPublished - 15 Mar 2016

Keywords

  • Centre
  • Global injectivity
  • Real Jacobian conjecture

Fingerprint Dive into the research topics of 'A sufficient condition in order that the real Jacobian conjecture in R<sup>2</sup> holds'. Together they form a unique fingerprint.

Cite this