JournalscmhVol. 83 , No. 1DOI 10.4171/cmh/115

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

  • Andrew Haas

    University of Connecticut, Storrs, United States
The distribution of geodesic excursions into the neighborhood of a cone singularity on a hyperbolic 2-orbifold cover

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 ≥ 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.