Jump to ContentJump to Main Navigation
Show Summary Details
More options …

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

See all formats and pricing
More options …
Volume 6, Issue 3


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


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.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Seon-Hee Lim
The Pure and Applied Mathematics, 2012, Volume 19, Number 1, Page 73

Comments (0)

Please log in or register to comment.
Log in