Logarithmic asymptotics for the number of periodic orbits of the Teichmüller flow on Veech's space of zippered rectangles

A logarithmic asymptotics is obtained for the number of periodic orbits of the Teichmüller flow on Veech's space of zippered rectangles, such that the norm of the corresponding renormalization matrix does not exceed a given value. The exponential growth rate of the number of such orbits is equal to the entropy of the flow.