Symbolic dynamics for the Teichmueller flow

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 $3g-3+m\geq 2$\mathrm{.}Weconstructasubshiftoffinitetype$(\Omega,\sigma)$ and a Borel suspension of $(\mathrm{\Omega },\sigma )$ which admits a finite-to-one semi-conjugacy into the Teichmueller flow ${\mathrm{\Phi }}^t$ on Q. This is used to show that the ${\mathrm{\Phi }}^t$-invariant Lebesgue measure on Q is the unique measure of maximal entropy.