Injectivity as a transversality phenomenon in geometries of negative curvature
type: Item
instance of: scholarly article
title: Injectivity as a transversality phenomenon in geometries of negative curvature
zbMATH Open document ID: 0965.58013
author: Frederico Xavier
published in: Illinois Journal of Mathematics
publication date: 2001-07-29T00:00:00Z
review text: The global asymptotic stability conjecture in dynamical systems was solved recently by Feller, Glutsiuk and Gutierrez. Crucial to the approach of \textit{C. Gutierrez} [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 12, No. 6, 627-671 (1995; Zbl 0837.34057)] is the following theorem of his: A local diffeomorphism \(f: \mathbb{R}^2\to \mathbb{R}^2\) for which the eigenvalues of \(Df(x)\) miss \((0,\infty)\) must be injective. The present paper gives a partial generalization of this theorem to local diffeomorphisms between Hadamard surfaces, the spectral conditions being replaced by transversality conditions among certain foliations associated to horocycles. The proofs use arguments from global analysis.
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 34A99
zbMATH DE Number: 1333063
zbMATH Keywords: injectivity
zbMATH Keywords: local diffeomorphism
zbMATH Keywords: Hadamard surfaces
zbMATH Keywords: transversality
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1333063