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

摘要

The logarithmic asymptotics for the growth of the number of periodic orbits,such that the norm of the corresponding renormalization matrix does not exceeda given constant, is computed for the Teichmueller flow on Veech's moduli spaceof zippered rectangles. The rate is equal to the entropy of the flow withrespect to the absolutely continuous invariant measure.