Groups, Geometry, and Dynamics

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Volume 8, Issue 3, 2014, pp. 883–932
DOI: 10.4171/GGD/252

Published online: 2014-10-02

Hyperbolic groupoids: metric and measure

Volodymyr V. Nekrashevych[1]

(1) Texas A&M University, College Station, United States

We construct Patterson–Sullivan measure and a natural metric on the unit space of a hyperbolic groupoid. In particular, this gives a new approach to defining SRB measures on Smale spaces and Anosov flows using Gromov hyperbolic graphs. Other results include a duality theory for hyperbolic groupoids graded by Hölder continuous Busemann cocycles, and a characterization of visual metrics.

Keywords: Patterson–Sullivan measure, visual metric, SRB measure, hyperbolic groupoids, hyperbolic graphs

Nekrashevych Volodymyr: Hyperbolic groupoids: metric and measure. Groups Geom. Dyn. 8 (2014), 883-932. doi: 10.4171/GGD/252