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Volume entropy of hyperbolic buildings

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.

preprint2009arXivOpen access
Francois LedrappierSeonhee Lim
math.GRmath.DS
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Francois LedrappierSeonhee Lim

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