Injectivity of differentiable maps ℝ² → ℝ² at infinity

Abstract.

The main result given in Theorem 1.1 is a condition for a map X, defined on the complement of a disk D in ℝ² with values in ℝ², to be extended to a topological embedding of ℝ², not necessarily surjective. The map X is supposed to be just differentiable with the condition that, for some ε > 0, at each point the eigenvalues of the differential do not belong to the real interval (-ε,∞). The extension is obtained by restricting X to the complement of some larger disc. The result has important connections with the property of asymptotic stability at infinity for differentiable vector fields.