A corrected proof shows that strong stable sets differ from horocyclic orbits for vectors on infinite hyperbolic surfaces whose geodesic rays encounter arbitrarily short closed geodesics.
Sasaki, On the differential geometry of tangent bundles of Riemannian manifolds, Tohoku Math
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Bellis strong stable sets on infinite hyperbolic surfaces
A corrected proof shows that strong stable sets differ from horocyclic orbits for vectors on infinite hyperbolic surfaces whose geodesic rays encounter arbitrarily short closed geodesics.