Patterson-Sullivan theory for groups with a strongly contracting element

TL;DR

This paper explores the growth behavior of groups acting on metric spaces with strongly contracting elements using Patterson-Sullivan measures, providing new insights into their geometric and dynamical properties.

Contribution

It introduces a novel application of Patterson-Sullivan theory to groups with strongly contracting elements, advancing understanding of their growth dynamics.

Findings

Established growth rate estimates for such groups

Connected contraction properties to measure-theoretic dynamics

Extended Patterson-Sullivan techniques to new group classes

Abstract

Using Patterson-Sullivan measures we investigate growth problems for groups acting on a metric space with a strongly contracting element.