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January  2010, 4(1): 139-165. doi: 10.3934/jmd.2010.4.139

Volume entropy of hyperbolic buildings

François Ledrappier 1, and  Seonhee Lim 2,

1. 

Department of Mathematics, 255 Hurley Hall, University of Notre Dame, Notre Dame IN 46556-4618
2. 

Department of Mathematical Sciences, Seoul National University, Seoul, 151-747, South Korea

Received  September 2009 Revised  March 2010 Published  May 2010

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, topological entropy, geodesic flow., volume entropy, volume growth.
Mathematics Subject Classification: Primary: 37D40, 37B40; Secondary: 20E4.
Citation: François Ledrappier, Seonhee Lim. Volume entropy of hyperbolic buildings. Journal of Modern Dynamics, 2010, 4 (1) : 139-165. doi: 10.3934/jmd.2010.4.139
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