On the measure with maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials (Q1002822)

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scientific article; zbMATH DE number 5519881
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On the measure with maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials
scientific article; zbMATH DE number 5519881

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    On the measure with maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials (English)
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    26 February 2009
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    The paper considers the Teichmüller flow \(g_t\) on the moduli space of abelian differentials with zeros of given orders on a Riemannian surface of a given genus. It is known that this flow preserves a finite absolutely continuous measure and is ergodic on every connected component \(\mathcal H\) of the moduli space. The main result of the paper is that \(\mu/\mu(\mathcal H)\) is the unique measure with maximal entropy for the restriction of \(g_t\) to \(\mathcal H\). The proof is based on the symbolic representation of \(g_t\).
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    moduli space
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    Teichmüller flow
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    suspension flow
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    topological Bernoulli shift
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    topological Markov shift
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    Markov-Bernoulli reduction
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