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arXiv · 1112.6107

Symbolic dynamics for the Teichmueller flow

Ursula Hamenstädt
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Abstract

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

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Ursula Hamenstädt. 2025-04-13. Symbolic dynamics for the Teichmueller flow. https://arxiv.org/abs/1112.6107

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