Existence and uniqueness of the measure of maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials

摘要

The main result of the paper is the statement that the 'smooth' measure of Masur and Veech is the unique measure of maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials. The proof is based on the symbolic representation of the flow in Veech's space of zippered rectangles.