A new qualitative proof of a result on the real jacobian conjecture

Francisco Braun, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

© 2015 Academia Brasileira de Ciencias. All rights reserved. Let F = (f, g) : ℝ2 → ℝ2 be a polynomial map such that det DF (x) is different from zero for all x ∈ ℝ2. We assume that the degrees of f and g are equal. We denote by f and g the homogeneous part of higher degree of (Formula presented) and (Formula presented), respectively. In this note we provide a proof relied on qualitative theory of differential equations of the following result: If (Formula presented) and (Formula presented) do not have real linear factors in common, then F is injective.
Original languageEnglish
Pages (from-to)1519-1524
JournalAnais da Academia Brasileira de Ciencias
Volume87
Issue number3
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Center
  • Global injectivity
  • Poincaré compactification
  • Real jacobian conjecture

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