2001/07/28 by Alex Eskin, Eskin, Alex, Howard Masur +3 · 1 citation
Mathematics · Physics and Astronomy · #37A99 (primary) 37E15 #37D40 #37D50 (secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics #math-ph #math.DS #math.MP #msc:37A99 #msc:37D40 #msc:37D50 #msc:37E15
paper · pdf · doi:10.48550/arxiv.math/0107204
arxiv created 2001/07/28 · openalex publication_date 2001/07/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use Ratner's theorem to compute the asymptotics of the number of (cylinders of) periodic trajectories in a rectangle with a barrier, assuming that the location p/q of the barrier is rational. We also show that as q tends to infinity, the constant in the asymptotic formula tends to the constant for the generic genus 2 flat surface.