The weak specification property for geodesic flows on $\mathrm{CAT}(–1)$ spaces

David Constantine; Jean-François Lafont; Daniel J. Thompson

doi:10.4171/ggd/545

JournalsggdVol. 14, No. 1pp. 297–336

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

David Constantine
Wesleyan University, Middletown, USA
Jean-François Lafont
Ohio State University, Columbus, USA
Daniel J. Thompson
Ohio State University, Columbus, USA

$The weak specification property for geodesic flows on $\mathrm{CAT}(–1)$ spaces cover$

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Abstract

We prove that the geodesic flow on a compact locally $CAT (-1)$ space has the weak specification 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 specification.

Cite this article

David Constantine, Jean-François Lafont, Daniel J. Thompson, The weak specification property for geodesic flows on $CAT (-1)$ spaces. Groups Geom. Dyn. 14 (2020), no. 1, pp. 297–336

DOI 10.4171/GGD/545