%0 Journal Article
%T Un lemme de Kazhdan-Margulis-Zassenhaus pour les g¨¦om¨¦tries de Hilbert
%A MickaŁżl Crampon
%A Ludovic Marquis
%J Mathematics
%D 2011
%I arXiv
%X We prove a Kazhdan-Margulis-Zassenhaus lemma for Hilbert geometries. More precisely, in every dimension $n$ there exists a constant $\varepsilon_n > 0$ such that, for any properly open convex set $\O$ and any point $x \in \O$, any discrete group generated by a finite number of automorphisms of $\O$, which displace $x$ at a distance less than $\varepsilon_n$, is virtually nilpotent.
%U http://arxiv.org/abs/1106.3156v3