We show that for every non-elementary hyperbolic group the Bowen-Margulis current associated with a strongly hyperbolic metric forms a unique group-invariant Radon measure class of maximal Hausdorff dimension on the boundary square. Applications include a characterization of roughly similar hyperbolic metrics via mean distortion.
Invariant measures of the topological flow and measures at infinity on hyperbolic groups
Tangents and slices of self-affine carpets
Typical behaviour along geodesic rays in hyperbolic groups
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