Diffeomorphisms of \(\mathbb{R}^ n\) with oscillatory Jacobians
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 \(x \in \mathbb{R}^ n\).
scientific article; zbMATH DE number 575434