Shadowing of actions of hyperbolic groups on their boundaries

TL;DR

This paper proves that hyperbolic groups' actions on their boundaries exhibit shadowing, ensuring topological stability, which enhances understanding of their dynamical properties.

Contribution

It establishes the shadowing property for hyperbolic groups' boundary actions, extending previous results on topological stability.

Findings

Hyperbolic groups' boundary actions have the shadowing property.

These actions are topologically stable.

The results unify and extend prior work by Mann et al.

Abstract

We prove that the canonical action of every hyperbolic group on its Gromov boundary has the shadowing (aka pseudo-orbit tracing) property. In particular, this recovers the results of Mann et al. that such actions are topologically stable.