Symbolic dynamics for the Teichmueller flow

Abstract

Let Q be a component of a stratum of abelian or quadratic differentials on an oriented surface of genus $g\ge 0$ with $m\ge 0$ punctures and $3g-3+m\ge 2$. We construct a subshift of finite type $(\Omega ,\sigma )$ and a Borel suspension of $(\Omega ,\sigma )$ which admits a finite-to-one semi-conjugacy into the Teichmueller flow ${\Phi }^t$ on Q. This is used to show that the ${\Phi }^t$-invariant Lebesgue measure on Q is the unique measure of maximal entropy.

arXiv commentCorrection of the last statement in Theorem 1, proofs are not affected. Details added, writing improved. 35p