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Groups, Geometry, and Dynamics


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Volume 14, Issue 1, 2020, pp. 297–336
DOI: 10.4171/GGD/545

Published online: 2020-02-27

The weak specification property for geodesic flows on CAT(–1) spaces

David Constantine[1], Jean-François Lafont[2] and Daniel J. Thompson[3]

(1) Wesleyan University, Middletown, USA
(2) Ohio State University, Columbus, USA
(3) Ohio State University, Columbus, USA

We prove that the geodesic flow on a compact locally CAT(−1) space has the weak speci fication property, and give various applications. We show that every Hölder potential on the space of geodesics has a unique equilibrium state. We establish the equidistribution of weighted periodic orbits and the large deviations principle for all such measures. The thermodynamic results are proved for the class of expansive flows with weak speci fication.

Keywords: CAT(–1) space, geodesic flow, weak specification property, equilibrium measure, Gibbs property, measure of maximal entropy, large deviations property

Constantine David, Lafont Jean-François, Thompson Daniel: The weak specification property for geodesic flows on CAT(–1) spaces. Groups Geom. Dyn. 14 (2020), 297-336. doi: 10.4171/GGD/545