Der Abbildungsgrad von Vektorfeldern zu stabilen Ruhelagen. (The topological degree of vector fields of stable equilibrium)
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.
scientific article; zbMATH DE number 4029998