Journal of Modern Dynamics (JMD)

Volume entropy of hyperbolic buildings

Pages: 139 - 165, Issue 1, January 2010      doi:10.3934/jmd.2010.4.139

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Fran├žois Ledrappier - Department of Mathematics, 255 Hurley Hall, University of Notre Dame, Notre Dame IN 46556-4618, United States (email)
Seonhee Lim - Department of Mathematical Sciences, Seoul National University, Seoul, 151-747, South Korea (email)

Abstract: 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.

Keywords:  building, volume entropy, volume growth, topological entropy, geodesic flow.
Mathematics Subject Classification:  Primary: 37D40, 37B40; Secondary: 20E42.

Received: September 2009;      Revised: March 2010;      Available Online: May 2010.