Excursion and return times of a geodesic to a subset of a hyperbolic Riemann surface

Haas, Andrew

doi:10.1090/S0002-9939-2013-11767-3

Excursion and return times of a geodesic to a subset of a hyperbolic Riemann surface
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Proc. Amer. Math. Soc. 141 (2013), 3957-3967 Request permission

Abstract:

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.

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