6 papers · 1 filter
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…
Comparison theorems for closed geodesics on negatively curved surfaces
Stephen Cantrell, Mark Pollicott
In this note we present new asymptotic estimates comparing the word length and geodesic length of closed geodesics on surfaces with (variable) negative sectional curvatures. In par…
Relative growth in hyperbolic groups
Stephen Cantrell, Richard Sharp
In this note we obtain estimates on the relative growth of normal subgroups of non-elementary hyperbolic groups, particularly those with free abelian quotient. As a corollary, we d…
Typical behaviour along geodesic rays in hyperbolic groups
Stephen Cantrell
In this note we study the limiting behaviour of real valued functions on hyperbolic groups as we travel along typical geodesic rays in the Gromov boundary of the group. Our results…
Statistical limit laws for hyperbolic groups
Stephen Cantrell
Using techniques from ergodic theory and symbolic dynamics, we derive statistical limit laws for real valued functions on hyperbolic groups. In particular, our results apply to con…
A Central Limit Theorem for Periodic Orbits of Hyperbolic Flows
Stephen Cantrell, Richard Sharp
We consider a counting problem in the setting of hyperbolic dynamics. Let be a weak mixing hyperbolic flow. We count the proportion of prime periodic orbits of …