2009/11/30 by Daniele D'Angeli, François Ledrappier, Seonhee Lim +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Entropy (arrow of time) #Geology #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Mathematics #Physics #Thermodynamics #Volume (thermodynamics) #math.DS #math.GR #msc:05C63 #msc:20E08 #msc:20F69 #msc:37E25
paper · pdf · doi:10.3934/jmd.2010.4.139
published as Journal of Modern Dynamics, Vol.4, No.1, 2010, 167-205 · 32 pages
openalex publication_date 2010/01/01 · arxiv created 2010/04/29 · arxiv updated 2015/03/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05
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.