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Asymptotic windings of horocycles. (English) Zbl 1407.37047
Summary: We analyze the scaling limits of the winding process for horocycles on noncompact hyperbolic surfaces with finite area. Initial conditions with precompact forward geodesics have scaling limits with gaussian and Cauchy components. Typical initial conditions have different scaling limits along different subsequences of times, and all such scaling limits can be described. Some of our results extend to other unipotent flows.

MSC:
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37E35 Flows on surfaces
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