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math.DS2022
Mixing of the Mineyev flow, orbital counting and Poincaré series for strongly hyperbolic metrics
Stephen Cantrell
We obtain orbital counting results for the class of strongly hyperbolic metrics on hyperbolic groups. To achieve this we combine ergodic theoretic techniques involving the Mineyev…
math.DS2022
Invariant measures of the topological flow and measures at infinity on hyperbolic groups
Stephen Cantrell, Ryokichi Tanaka
We show that for every non-elementary hyperbolic group, an associated topological flow space admits a coding based on a transitive subshift of finite type. Applications include reg…
math.DS2022
Counting and boundary limit theorems for representations of Gromov-hyperbolic groups
Stephen Cantrell, Cagri Sert
Given a Gromov-hyperbolic group endowed with a finite symmetric generating set, we study the statistics of counting measures on the spheres of the associated Cayley graph under…