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

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

2011-08-24

arxiv.org/abs/1108.4957v1

Mathematics

Dynamical Systems

13 pages, 1 figure

Scientific paper

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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