  A real matrix is Hurwitz if its eigenvalues have negative real parts. The
following generalisation of the Bidimensional Global Asymptotic Stability
Problem (BGAS) is provided: Let $X:R^2-->R^2$ be a C^1 vector field whose
derivative DX(p) is Hurwitz for almost all p in $R^2$. Then the singularity set
of X, Sing(X), is either an emptyset, a one--point set or a non-discrete set.
Moreover, if Sing(X) contains a hyperbolic singularity then X is topologically
equivalent to the radial vector field $(x,y)--> (-x,-y)$. This generalises BGAS
to the case in which the vector field is not necessarily a local
diffeomorphism.

Dynamical Systems