Functional Analysis and Its Applications

, Volume 42, Issue 3, pp 224–226 | Cite as

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



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 words

moduli space Teichmüller flow suspension flow topological Bernoulli shift topological Markov shift Markov-Bernoulli reduction 


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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Rice UniversityHoustonUSA
  2. 2.Moscow State University, Institute for Problems of Information TransmissionRussian Academy of SciencesMoscowRussia

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