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Free, publicly-accessible full text available June 1, 2026
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A hyperbolic group \Gammaacts by homeomorphisms on its Gromov boundary\partial \Gamma. We use a dynamical coding of boundary points to show that such actions aretopologically stablein the dynamical sense: any nearby action is semi-conjugate to (and an extension of) the standard boundary action. This result was previously known in the special case that\partial \Gammais a topological sphere. Our proof here is independent and gives additional information about the semi-conjugacy in that case. Our techniques also give a new proof of global stability when\partial \Gamma = S^{1}.more » « lessFree, publicly-accessible full text available March 17, 2026
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Free, publicly-accessible full text available January 1, 2026
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