Geodesic
On the Measure with Maximal Entropy for the Teichm\"uller Flow on the Moduli Space of Abelian Differentials
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 3, pp. 75-77

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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 $\mathcal H$ 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 $g_t$.
Mots-clés : moduli space
Keywords: Teichmüller flow, suspension flow, topological Bernoulli shift, topological Markov shift, Markov–Bernoulli reduction. 
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     author = {A. I. Bufetov and B. M. Gurevich},
     title = {On the {Measure} with {Maximal} {Entropy} for the {Teichm\"uller} {Flow} on the {Moduli} {Space} of {Abelian} {Differentials}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {75--77},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2008_42_3_a7/}
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A. I. Bufetov; B. M. Gurevich. On the Measure with Maximal Entropy for the Teichm\"uller Flow on the Moduli Space of Abelian Differentials. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 3, pp. 75-77. http://geodesic.mathdoc.fr/item/FAA_2008_42_3_a7/