Individual Closed Horocyclic Orbits on the Modular Surface
  We track the trajectories of individual horocycles on the modular surface. Our tracking is constructive, and we thus \emph{effectively} establish topological transitivity and even line-transitivity for the horocyclic flow. We also describe homotopy class jumps that occur under continuous deformation of horocycles. 
Marvin Knopp and Mark Sheingorn
math.NT math.DS