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arXiv · 1108.4957

On a weak Jelonek's real Jacobian Conjecture in $\R^n$

Alexandre Fernandes·Carlos Maquera·Jean Venato Santos
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Abstract

Let $Y:\R^n\to\R^n$ be a polynomial local diffeomorphism and let $S_Y$ denote the set of not proper points of $Y$. The Jelonek's real Jacobian Conjecture states that if $\codim(S_Y)\geq2$, then $Y$ is bijective. We prove a weak version of such conjecture establishing the sufficiency of a necessary condition for bijectivity. Furthermore, we generalize our result on bijectivity to semialgebraic local diffeomorphisms.

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Alexandre Fernandes, Carlos Maquera, Jean Venato Santos. 2011-08-24. On a weak Jelonek's real Jacobian Conjecture in $\R^n$. https://arxiv.org/abs/1108.4957

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