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We show that for every non-elementary hyperbolic group, an associatedtopological flow space admits a coding based on a transitive subshift of finitetype. Applications include regularity results for Manhattan curves, theuniqueness of measures of maximal Hausdorff dimension with potentials, and thereal analyticity of intersection numbers for families of dominatedrepresentation, thus providing a direct proof of a result established byBridgeman et al. in 2015.

Invariant measures of the topological flow and measures at infinity on hyperbolic groups