Density of half-horocycles on geometrically infinite hyperbolic surfaces (Q2842232)

The author extends her earlier results from [J. Lond. Math. Soc., II. Ser. 84, No. 3, 785--806 (2011; Zbl 1263.37012)] to include geometrically infinite surfaces: a vector whose full horocyclic orbit is dense on a non-elementary geometrically infinite oriented hyperbolic surface has both half-orbits (forward and backward) dense if the geodesic flow intersects infinitely many closed geodesic of bounded length at an angle bounded away from zero (Theorem 1.2). The necessity of this assumption is exhibited in Theorem 1.3, a construction in which the bound on the lengths of the closed geodesics is removed and the resulting horocycle is only dense in one direction.