Volume entropy of hyperbolic buildings

Details Volume entropy of hyperbolic buildings Volume entropy of hyperbolic buildings

2009-02-06

arxiv.org/abs/0902.1168v2

Mathematics

Dynamical Systems

25 pages, 4 figures

Scientific paper

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.

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