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 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 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.

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