Geodesic
Hyperbolic groupoids: metric and measure
Volodymyr V. Nekrashevych1 orcid
1Texas A&M University, College Station, United States
Groups, geometry, and dynamics, Tome 8 (2014) no. 3, pp. 883-932

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DOI

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.
DOI : 10.4171/ggd/252
Classification : 00-XX
Mots-clés : Patterson–Sullivan measure, visual metric, SRB measure, hyperbolic groupoids, hyperbolic graphs

Volodymyr V. Nekrashevych  1

1 Texas A&M University, College Station, United States 
Volodymyr V. Nekrashevych. Hyperbolic groupoids: metric and measure. Groups, geometry, and dynamics, Tome 8 (2014) no. 3, pp. 883-932. doi: 10.4171/ggd/252
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     title = {Hyperbolic groupoids: metric and measure},
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     pages = {883--932},
     year = {2014},
     volume = {8},
     number = {3},
     doi = {10.4171/ggd/252},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/252/}
}
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