Der Abbildungsgrad von Vektorfeldern zu stabilen Ruhelagen. (The topological degree of vector fields of stable equilibrium)
type: Item
instance of: scholarly article
title: Der Abbildungsgrad von Vektorfeldern zu stabilen Ruhelagen. (The topological degree of vector fields of stable equilibrium)
zbMATH Open document ID: 0633.34027
DOI: 10.1007/BF01197974
author: Klaus Thews
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: Let f denote a differentiable vector field on \({\mathbb{R}}^ n\) such that \(f(0)=0\) and 0 is an isolated zero. It is shown that the Brouwer-degree of -f at 0 equals 1 provided 0 is a stable equilibrium of the flow generated by f (and if some additional assumptions hold in the case \(n\geq 3)\). As an application it is demonstrated that certain instabilities in the holomorphic case studied by Goetz and Turdy are in some sense robust against moderate, non-holomorphic perturbations of f.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A99
zbMATH DE Number: 4029998
zbMATH Keywords: topological degree
zbMATH Keywords: Brouwer-degree
zbMATH Keywords: stable equilibrium
MaRDI profile type: Publication
cites work: Q5727924
cites work: Stabilität der Gleichgewichtslösung komplexer Differentialgleichungssysteme
cites work: The Operator of Translation Along the Trajectories of Differential Equations
cites work: Q5595388
description: scientific article; zbMATH DE number 4029998