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Tr. Mat. Inst. Steklova, 2000, Volume 231, Pages 119–133 (Mi tm514)  

This article is cited in 5 scientific papers (total in 5 papers)

An Ergodic Theorem for the Action of a Free Semigroup

R. I. Grigorchuk


Abstract: An individual ergodic theorem for the action of a free semigroup is proved under the assumption that the measure is stationary. The proof involves the constructions of the associated stationary Markov process and of the skew shift.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2000, 231, 113–127

Bibliographic databases:
UDC: 517.987+519.217
Received in May 2000

Citation: R. I. Grigorchuk, “An Ergodic Theorem for the Action of a Free Semigroup”, Dynamical systems, automata, and infinite groups, Collected papers, Tr. Mat. Inst. Steklova, 231, Nauka, MAIK Nauka/Inteperiodika, M., 2000, 119–133; Proc. Steklov Inst. Math., 231 (2000), 113–127

Citation in format AMSBIB
\Bibitem{Gri00}
\by R.~I.~Grigorchuk
\paper An Ergodic Theorem for the Action of a~Free Semigroup
\inbook Dynamical systems, automata, and infinite groups
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2000
\vol 231
\pages 119--133
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm514}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1841754}
\zmath{https://zbmath.org/?q=an:1172.37303}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2000
\vol 231
\pages 113--127


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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. Misiurewicz M., Rodrigues A., “Real 3x+1”, Proceedings of the American Mathematical Society, 133:4 (2005), 1109–1118  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Bufetov A.I., Series C., “A pointwise ergodic theorem for Fuchsian groups”, Math Proc Cambridge Philos Soc, 151:1 (2011), 145–159  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    3. A. I. Bufetov, A. V. Klimenko, “Maximal inequality and ergodic theorems for Markov groups”, Proc. Steklov Inst. Math., 277 (2012), 27–42  mathnet  crossref  mathscinet  isi  elib  elib
    4. Bufetov A., Klimenko A., “On Markov Operators and Ergodic Theorems for Group Actions”, Eur. J. Comb., 33:7, SI (2012), 1427–1443  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. Bowen L., Bufetov A., Romaskevich O., “Mean convergence of Markovian spherical averages for measure-preserving actions of the free group”, Geod. Dedic., 181:1 (2016), 293–306  crossref  mathscinet  zmath  isi  scopus
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