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patterson–sullivan measure

Ergodic Theory and Dynamical Systems (1)

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Topological flows for hyperbolic groups
Part of
- Special aspects of infinite or finite groups
- Dynamical systems with hyperbolic behavior
RYOKICHI TANAKA
Journal:

Ergodic Theory and Dynamical Systems / Volume 41 / Issue 11 / November 2021

Published online by Cambridge University Press:

30 October 2020, pp. 3474-3520

Print publication:

November 2021
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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.