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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard


IMPACT FACTOR 2018: 0.789

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.329
Source Normalized Impact per Paper (SNIP) 2018: 0.908

Mathematical Citation Quotient (MCQ) 2018: 0.53

Online
ISSN
1615-7168
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Volume 6, Issue 3

Issues

Entropy of the geodesic flow for metric spaces and Bruhat–Tits buildings

Enrico Leuzinger
Published Online: 2006-08-10 | DOI: https://doi.org/10.1515/ADVGEOM.2006.029

Abstract

Let (X, dX ) be a geodesically complete Hadamard space endowed with a Borel-measure μ. Assume that there exists a group Γ of isometries of X which acts totally discontinuously and cocompactly on X and preserves μ. We show that the topological entropy of the geodesic flow on the space of (parametrized) geodesics of the compact quotient Γ\X is equal to the volume entropy of μ (if X satisfies a certain local uniformity condition). This extends a result of Manning for riemannian manifolds of nonpositive curvature to the singular case. The result in particular holds for Bruhat–Tits buildings, for which we also compute the entropy explicitly.

Key words: topological entropy; geodesic flow; Hadamard spaces; Bruhat–Tits buildings; discrete subgroups of Lie groups; p-adic groups

About the article


Received: 2005-06-28

Revised: 2005-10-18

Published Online: 2006-08-10

Published in Print: 2006-07-01


Citation Information: Advances in Geometry, Volume 6, Issue 3, Pages 475–491, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/ADVGEOM.2006.029.

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