Injectivity of differentiable maps R2→R2 at infinity
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.
Autor(es):Gutierrez, Carlos;
Rabanal, Roland
Año: 2006
Título de la revista: Bulletin of the Brazilian Mathematical Society
Volumen: 37
Página inicial - Página final: 217-239
ISSN: 1678-7544
Url: http://link.springer.com/article/10.1007%2Fs00574-006-0011-4