Shadowing of actions of hyperbolic groups on their boundaries

2024/05/08 by Doucha, Michal
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2405.04905

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.

Related

• Shadowing for actions of some finitely generated groups
• Stability of hyperbolic groups acting on their boundaries
• Stability for hyperbolic groups acting on boundary spheres
• Characterization of hyperbolicity and generalized shadowing lemma
• C0-Stability for actions implies shadowing property