We calculate the asymptotic average rate at which a generic geodesic on a finite area hyperbolic 2-orbifold returns to a subsurface with geodesic boundary. As a consequence we get the average time a generic geodesic spends in such a subsurface. Related results are obtained for excursions into a collar neighborhood of a simple closed geodesic and the associated distribution of excursion depths.
Local limit theorems for hitting times and return times of small sets
Return times, recurrence densities and entropy for actions of some discrete amenable groups
Convergence of Rare Events Point Processes to the Poisson for billiards
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