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.
Bellis, ´Etude topologique du flot horocyclique: le cas des surfaces g´ eom´ etriquement infinies, PhD thesis, Institut de Recherche Math´ ematique de Rennes
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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.