BROISE-ALAMICHEL, Anne - Topologie et Dynamique, Université Paris-Sud, Bât. 425, 91405 Orsay cedex
PAULIN, Frédéric - ENS, 45 rue d'Ulm, 75230 Paris cedex

Abstract :

Given a tree $T$ and a group $\Gamma$ of automorphisms of $T$, we study the markovian properties of the geodesic flow on the quotient by $\Gamma$ of the space of geodesics of $T$. For instance, when $T$ is the Bruhat-Tits tree of a semi-simple connected algebraic group $\underline{G}$ of rank one over a non archimedian local field $\wh K$, and $\Gamma$ is a (possibly non uniform) lattice in $\underline{G}(\wh K)$, we prove that the type preserving geodesic flow is Bernoulli.

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Contact : Anne.Broise@math.u-psud.fr