A sufficient condition in order that the real Jacobian conjecture in \(\mathbb{R}^2\) holds
type: Item
instance of: scholarly article
title: A sufficient condition in order that the real Jacobian conjecture in \(\mathbb{R}^2\) holds
zbMATH Open document ID: 1332.14072
author: Francisco Braun
author: Jaume Giné
author: Jaume Llibre
published in: Journal of Differential Equations
publication date: 2016-01-26T00:00:00Z
review text: The author gives a partial result concerning the real Jacobian conjecture in \(\mathbb{R}^{2}:\) if \(F=(f,g):\mathbb{R}^{2}\mathbb{\rightarrow R}^{2}\) is a polynomial map such that \(\det DF\) is nowhere zero, \(F(0,0)=(0,0),\) and the higher homogeneous terms of the polynomials \(ff_{x}+gg_{x}\) and \( ff_{y}+gg_{y}\) do not have real linear factors in common, then \(F\) is injective.
Mathematics Subject Classification ID: 14R15
Mathematics Subject Classification ID: 35F05
zbMATH DE Number: 6535788
zbMATH Keywords: real Jacobian conjecture
zbMATH Keywords: centre of a vector field
zbMATH Keywords: Hamiltonian vector field
reviewed by: Tadeusz Krasiński
MaRDI profile type: Publication
full work available at URL: j.jde.2015.12.011
OpenAlex ID: W2263607864
Wikidata QID: Q123240723
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DOI: 10.1016/J.JDE.2015.12.011
description: scientific article; zbMATH DE number 6535788