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math.DS2025
The Manhattan curve, ergodic theory of topological flows and rigidity
Stephen Cantrell, Ryokichi Tanaka
For every non-elementary hyperbolic group, we introduce the Manhattan curve associated to any pair of left-invariant hyperbolic metrics which are quasi-isometric to a word metric.…
math.DS2025
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.DS2024
Central limit theorems for Green metrics on hyperbolic groups
Stephen Cantrell, Mark Pollicott
Suppose we have two finitely supported, admissible, probability measures on a hyperbolic group . In this article we prove that the corresponding two Green metrics satisfy a cou…