Volume entropy of hyperbolic buildings

F. Ledrappier (1) , S. Lim

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We characterize the volume entropy of a regular building as the topological pressure of the geodesic flow on an apartment. We show that the entropy maximizing measure is not Liouville measure for any regular hyperbolic building. As a consequence, we obtain a strict lower bound on the volume entropy in terms of the branching numbers and the volume of the boundary polyhedrons.

Domaines: Probabilités [math.PR]

F. Ledrappier, S. Lim. Volume entropy of hyperbolic buildings. Journal of modern dynamics, 2010, 4 (1), pp.139-165. ⟨10.3934/jmd.2010.4.139⟩. ⟨hal-00497032⟩