A sufficient condition for the real Jacobian conjecture in R2. (August 2021)

• Record Type: Journal Article
• Authors: Llibre, Jaume; Valls, Claudia
• Is Part Of: Nonlinear analysis. Volume 60(2021)
• Publication Date: 2021-08
• Subjects: Real Jacobian conjecture -- Global injectivity -- Center; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103298
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Let F = ( f, g ) : R 2 → R 2 be a polynomial map such that det D F ( x, y ) is different from zero for all ( x, y ) ∈ R 2 . We provide some new sufficient conditions for the injectivity of F . The proofs are based on the qualitative theory of differential equations.