On the measure with maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials
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The Teichmüller flow gt on the moduli space of Abelian differentials with zeros of given orders on a Riemann surface of a given genus is considered. This flow is known to preserve a finite absolutely continuous measure and is ergodic on every connected component ℋ of the moduli space. The main result of the paper is that µ/µ(ℋ) is the unique measure with maximal entropy for the restriction of gt to ℋ. The proof is based on the symbolic representation of gt.
Key wordsmoduli space Teichmüller flow suspension flow topological Bernoulli shift topological Markov shift Markov-Bernoulli reduction
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