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Volume entropy of hyperbolic buildings

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  • 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.
    Mathematics Subject Classification: Primary: 37D40, 37B40; Secondary: 20E42.

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