The distribution of geodesic excursions into the neighborhood of a cone singularity on a hyperbolic 2-orbifold

Abstract

A generic geodesic on a finite area, hyperbolic 2-orbifold exhibits an infinite sequence of penetrations into a neighborhood of a cone singularity of order $k\ge 3$, so that the sequence of depths of maximal penetration has a limiting distribution. The distribution function is the same for all such surfaces and is described by a fairly simple formula.