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Uspekhi Mat. Nauk, 2013, Volume 68, Issue 5(413), Pages 3–80 (Mi umn9557)  

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

Limit theorems for suspension flows over Vershik automorphisms

A. I. Bufetovabcd

a Steklov Mathematical Institute of the Russian Academy of Sciences
b Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences
c National Research University "Higher School of Economics"
d Laboratoire d'Analyse, Topologie, Probabilités, Aix-Marseille Université, CNRS

Abstract: In this paper an asymptotic expansion of ergodic integrals for suspension flows over Vershik automorphisms is obtained and a limit theorem for these flows is given.
Bibliography: 49 titles.

Keywords: Vershik automorphisms, renormalization, rate of convergence in the ergodic theorem, limit theorems, finitely additive invariant measures, Teichmüller flow, Forni invariant distributions, Kontsevich–Zorich cocycle.

Funding Agency Grant Number
Agence Nationale de la Recherche ANR-11-IDEX-0001-02
Alfred P. Sloan Foundation
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Ministry of Education and Science of the Russian Federation МК-4893.2010.1
МК-6734.2012.1
Russian Foundation for Basic Research 11-01-00654
12-01-33020
12-01-31284
10-01-93115-НЦНИЛ
National Science Foundation DMS 0604386
Rice University


DOI: https://doi.org/10.4213/rm9557

Full text: PDF file (1145 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2013, 68:5, 789–860

Bibliographic databases:

UDC: 517.987.5+517.938+519.21
MSC: 37A50, 37E35, 37B10, 60Fxx
Received: 20.02.2012

Citation: A. I. Bufetov, “Limit theorems for suspension flows over Vershik automorphisms”, Uspekhi Mat. Nauk, 68:5(413) (2013), 3–80; Russian Math. Surveys, 68:5 (2013), 789–860

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Bufetov, B. Solomyak, “On the modulus of continuity for spectral measures in substitution dynamics”, Adv. Math., 260 (2014), 84–129  crossref  mathscinet  zmath  isi  elib  scopus
    2. Alexander I. Bufetov, “Finitely-additive measures on the asymptotic foliations of a Markov compactum”, Mosc. Math. J., 14:2 (2014), 205–224  mathnet  crossref  mathscinet  elib
    3. A. Borodin, L. Petrov, “Integrable probability: from representation theory to Macdonald processes”, Probab. Surv., 11 (2014), 1–58  crossref  mathscinet  zmath  elib  scopus
    4. Dmitry Zubov, “On cohomological equations for suspension flows over Vershik automorphisms”, Mosc. Math. J., 16:2 (2016), 381–391  mathnet  crossref  mathscinet  elib
    5. K. Lindsey, R. Trevino, “Infinite type flat surface models of ergodic systems”, Discrete Contin. Dyn. Syst., 36:10 (2016), 5509–5553  crossref  mathscinet  zmath  isi  elib  scopus
    6. J. Fickenscher, “Decoding Rauzy induction: an answer to Bufetov's general question”, Bull. Soc. Math. France, 145:4 (2017), 603–621  crossref  mathscinet  zmath  isi  scopus
    7. A. I. Bufetov, B. Solomyak, “The Hölder property for the spectrum of translation flows in genus two”, Isr. J. Math., 223:1 (2018), 205–259  crossref  mathscinet  zmath  isi  scopus
    8. R. Treviño, “Flat surfaces, Bratteli diagrams and unique ergodicity à la Masur”, Israel J. Math., 225:1 (2018), 35–70  crossref  mathscinet  zmath  isi  scopus
    9. Hooper W.P., Trevino R., “Indiscriminate Covers of Infinite Translation Surfaces Are Innocent, Not Devious”, Ergod. Theory Dyn. Syst., 39:8 (2019), 2071–2127  crossref  isi
    10. A. Klimenko, “Prostranstvennaya predelnaya teorema dlya perekladyvanii otrezkov”, Mosc. Math. J., 19:2 (2019), 343–356  mathnet  crossref  mathscinet
    11. Berlinkov A., Solomyak B., “Singular Substitutions of Constant Length”, Ergod. Theory Dyn. Syst., 39:9 (2019), 2384–2402  crossref  isi
    12. Bufetov A.I., Solomyak B., “A Spectral Cocycle For Substitution Systems and Translation Flows”, J. Anal. Math., 141:1 (2020), 165–205  crossref  mathscinet  zmath  isi
  • Успехи математических наук Russian Mathematical Surveys
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