Injectivity of differentiable maps R^2 --> R^2 at infinity

Details Injectivity of differentiable maps R^2 --> R^2 at infinity Injectivity of differentiable maps R^2 --> R^2 at infinity

2006-01-13

arxiv.org/abs/math/0601325v2

Mathematics

Dynamical Systems

to appear in Bulletin of the Brazilian Mathematical Society

Scientific paper

The main result given in Theorem~1.1 is a condition for a map $X$, defined on the complement of a disk $D$ in R^2 with values in R^2, to be extended to a topological embedding of R^2, not necessarily surjective. The map $X$ is supposed to be just differentiable with the condition that, for some $e>0,$ at each point the eigenvalues of the differential do not belong to the real interval $(-e,\infty).$ 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.

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