Hyperbolic groupoids: metric and measure Academic Article

abstract

• 2014 EMS Publishing House. All rights reserved. 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 Hlder continuous Busemann cocycles, and a characterization of visual metrics.

authors

• Nekrashevych, Volodymyr

published proceedings

• GROUPS GEOMETRY AND DYNAMICS

author list (cited authors)

• Nekrashevych, V.

citation count

• 2

complete list of authors

• Nekrashevych, Volodymyr

publication date

• January 2014

publisher

• European Mathematical Society - EMS - Publishing House GmbH  Publisher

published in

• Groups, Geometry, and Dynamics  Journal

keywords

• Hyperbolic Graphs
• Hyperbolic Groupoids
• Patterson-sullivan Measure
• Srb Measure
• Visual Metric

Digital Object Identifier (DOI)

• 10.4171/GGD/252

start page

• 883

end page

• 932

volume

• 8

issue

• 3

URL

• http://dx.doi.org/10.4171/ggd/252