Asymptotic stability at infinity for bidimensional Hurwitz vector fields

Abstract

Let $X:U-->R^2$ be a differentiable vector field. Set $Spc(X)=eigenvaluesofDX(z):z\in U$. This $X$ is called Hurwitz if $Spc(X)\subset z\in C:\Re (z)<0$. Suppose that $X$ is Hurwitz and $U\subset R^2$ is the complement of a compact set. Then by adding to $X$ a constant $v$ one obtains that the infinity is either an attractor or a repellor for $X+v.$

The paper was amended because the original version had an error