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 ≥ 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.
Cite this article
Andrew Haas, The distribution of geodesic excursions into the neighborhood of a cone singularity on a hyperbolic 2-orbifold. Comment. Math. Helv. 83 (2008), no. 1, pp. 1–20DOI 10.4171/CMH/115