Logarithmic asymptotics for the number of periodic orbits of the   Teichmueller flow on Veech's space of zippered rectangles
  The logarithmic asymptotics for the growth of the number of periodic orbits, such that the norm of the corresponding renormalization matrix does not exceed a given constant, is computed for the Teichmueller flow on Veech's moduli space of zippered rectangles. The rate is equal to the entropy of the flow with respect to the absolutely continuous invariant measure. 
Alexander I. Bufetov