Geodesic
Stability for hyperbolic groups acting on boundary spheres
Forum of Mathematics, Sigma, Tome 11 (2023)

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A hyperbolic group G acts by homeomorphisms on its Gromov boundary. We show that if $\partial G$ is a topological n–sphere, the action is topologically stable in the dynamical sense: any nearby action is semi-conjugate to the standard boundary action. 
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     author = {Kathryn Mann and Jason Fox Manning},
     title = {Stability for hyperbolic groups acting on boundary spheres},
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Kathryn Mann; Jason Fox Manning. Stability for hyperbolic groups acting on boundary spheres. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.78

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