On the measure with maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials
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The Teichmüller flow g t 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 g t to ℋ. The proof is based on the symbolic representation of g t .
Key wordsmoduli space Teichmüller flow suspension flow topological Bernoulli shift topological Markov shift Markov-Bernoulli reduction
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