Pseudo-Anosov flows on 3-manifolds induce isometric actions on Gromov-hyperbolic spaces, with generic elements in the fundamental group for non-R-covered flows.
Random walks on weakly hyperbolic groups
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Pseudo-Anosov flows and the geometry of Anosov-like group actions
Pseudo-Anosov flows on 3-manifolds induce isometric actions on Gromov-hyperbolic spaces, with generic elements in the fundamental group for non-R-covered flows.