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Topology of horocycles on geometrically finite nonpositively curved surfaces (2312.07719v2)
Published 12 Dec 2023 in math.DS
Abstract: We study the closure of horocycles on rank 1 nonpositively curved surfaces with finitely generated fundamental group. Each horocycle is closed or dense on a certain subset of the unit tangent bundle. In fact, we classify each half-horocycle in terms of the associated geodesic rays. We also determine the nonwandering set of the horocyclic flow and characterize the surfaces admitting a minimal set for this flow.