Volume entropy of hyperbolic buildings
Dynamical Systems
2012-12-14 v2 Group Theory
Abstract
We characterize the volume entropy of an arbitrary regular building as the topological pressure of the geodesic flow on an apartment. We show that the Liouville measure is not entropy maximizing measure for regular hyperbolic buildings. 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.
Cite
@article{arxiv.0902.1168,
title = {Volume entropy of hyperbolic buildings},
author = {Francois Ledrappier and Seonhee Lim},
journal= {arXiv preprint arXiv:0902.1168},
year = {2012}
}
Comments
25 pages, 4 figures