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Mat. Sb., 2011, Volume 202, Number 7, Pages 3–42 (Mi msb7739)  

This article is cited in 12 scientific papers (total in 12 papers)

Existence and uniqueness of the measure of maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials

A. I. Bufetovab, B. M. Gurevichcd

a Steklov Mathematical Institute, Russian Academy of Sciences
b Department of Mathematics, Rice University, Houston, TX, USA
c M. V. Lomonosov Moscow State University
d A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: The main result of the paper is the statement that the ‘smooth’ measure of Masur and Veech is the unique measure of maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials. The proof is based on the symbolic representation of the flow in Veech's space of zippered rectangles.
Bibliography: 29 titles.

Keywords: moduli space, Rauzy induction, symbolic dynamics, Markov shift, suspension flow.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7739

Full text: PDF file (810 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2011, 202:7, 935–970

Bibliographic databases:

UDC: 517.938
MSC: 28D20, 37A35, 37D, 37E35
Received: 13.05.2010 and 21.11.2010

Citation: A. I. Bufetov, B. M. Gurevich, “Existence and uniqueness of the measure of maximal entropy for the Teichmüller flow on the moduli space of Abelian differentials”, Mat. Sb., 202:7 (2011), 3–42; Sb. Math., 202:7 (2011), 935–970

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Climenhaga V., Thompson D.J., “Intrinsic ergodicity beyond specification: $\beta$-shifts, $S$-gap shifts, and their factors”, Israel J. Math., 192:2 (2012), 785–817  crossref  mathscinet  zmath  isi  scopus
    2. G. Iommi, Th. Jordan, “Phase transitions for suspension flows”, Commun. Math. Phys., 320:2 (2013), 475–498  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. A. I. Bufetov, “Limit theorems for suspension flows over Vershik automorphisms”, Russian Math. Surveys, 68:5 (2013), 789–860  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. Bufetov, “Limit theorems for translation flows”, Ann. Math., 179:2 (2013), 431–499  crossref  mathscinet  isi  scopus
    5. U. Hamenstädt, “Bowen's construction for the Teichmüller flow”, J. Mod. Dyn., 7:4 (2013), 489–526  crossref  mathscinet  zmath  isi  scopus
    6. B. M. Gurevich, “A lower estimate of the entropy of an automorphism and maximum entropy conditions for and invariant measure of a suspension flow over a Markov shift”, Dokl. Math., 91:2 (2015), 186–188  crossref  crossref  zmath  isi  elib  elib  scopus
    7. B. Gurevich, “On a measure with maximal entropy for a suspension flow over a countable alphabet Markov shift”, Eur. J. Math., 1:3 (2015), 545–559  crossref  mathscinet  zmath  scopus
    8. A. Avila, P. Hubert, A. Skripchenko, “Diffusion for chaotic plane sections of 3-periodic surfaces”, Invent. Math., 206:1 (2016), 109–146  crossref  mathscinet  zmath  isi  scopus
    9. Aimino R., Nicol M., Todd M., “Recurrence Statistics For the Space of Interval Exchange Maps and the Teichmüller Flow on the Space of Translation Surfaces”, Ann. Inst. Henri Poincare-Probab. Stat., 53:3 (2017), 1371–1401  crossref  mathscinet  zmath  isi  scopus
    10. Iommi G., Riquelme F., Velozo A., “Entropy in the Cusp and Phase Transitions For Geodesic Flows”, Isr. J. Math., 225:2 (2018), 609–659  crossref  mathscinet  zmath  isi  scopus
    11. Eskin A., Mirzakhani M., “Invariant and Stationary Measures For the Sl(2, R) Action on Moduli Space”, Publ. Math. IHES, 2018, no. 127, 95–324  crossref  mathscinet  isi  scopus
    12. Climenhaga V., “Specification and Towers in Shift Spaces”, Commun. Math. Phys., 364:2 (2018), 441–504  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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