Diffeomorphisms of \(\mathbb{R}^ n\) with oscillatory Jacobians
type: Item
instance of: scholarly article
title: Diffeomorphisms of \(\mathbb{R}^ n\) with oscillatory Jacobians
zbMATH Open document ID: 0816.15021
DOI: 10.5565/PUBLMAT_37293_02
author: Nelson M. Kuhl
author: Waldyr Muniz Oliva
author: Luis T. Magalhães
published in: Publicacions Matemàtiques
publication date: 1995-07-23T00:00:00Z
full work available at URL: https://eudml.org/doc/41530
review text: A square matrix \(A\) with real entries is called totally positive (resp. strictly totally positive) if all its minors are nonnegative (resp. positive). It is called oscillatory if it is totally positive and if some power of \(A\) is strictly totally positive. The main achievements of the article are a new proof of a theorem of Gantmacher-Krein on the spectral properties of oscillatory matrices and a result on diffeomorphisms \(f\) of \(\mathbb{R}^ n\) for which \(f'(x)\) is oscillatory for every \(x \in \mathbb{R}^ n\).
reviewed by: Otto Liess
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 57R50
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 575434
zbMATH Keywords: oscillatory Jacobians
zbMATH Keywords: oscillatory matrix
zbMATH Keywords: transversality theorem
zbMATH Keywords: strictly totally positive matrix
zbMATH Keywords: spectral properties
zbMATH Keywords: diffeomorphisms
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 575434