A179/2002 - On local diffeomorphisms of R^n that are injective

Preprint A179/2002

On local diffeomorphisms of R^n that are injective

Carlos Gutierrez | Fernandes, Alexandre

Keywords: Marcus Yamabe Conjecture | Jacobian Conjecture | assimptotic stability | global injectivity

Let $X\colon \R^2 \rightarrow \R^2$ be a map of class $C^1$ and let $\spec(X)$ be the set of (complex) eigenvalues of the derivative $DX_p$ when $p$ varies in $\R^2$. If, for some $\epsilon>0,$ $\spec(X)\cap [0,\epsilon)=\emptyset ,$ then $X$ is injective. Some partial extensions of this result to $\R^n$ will be presented.