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Moscow Mathematical Journal, 2019, Volume 19, Number 1, Pages 77–88
DOI: https://doi.org/10.17323/1609-4514-2019-19-1-77-88 (Mi mmj701) 		 
Random averaging in ergodic theorem

B. M. Gurevicha, S. A. Komechb, A. A. Tempelmanb

a Dept. Mech. and Math. Moscow State University, 119991 GSP-1, Moscow, Russia
b IITP RAS, Bolshoy Karetny per. 19, build. 1, Lab. 4, Moscow 127051 Russia
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DOI: https://doi.org/10.17323/1609-4514-2019-19-1-77-88
Abstract: For some symbolic dynamical systems we study the value of the boundary deformation for a small ball in the phase space during a period of time depending on the center and radius of the ball. For actions of countable Abelian groups, a version of the Mean Ergodic theorem with averaging over random sets is proved and used in the proof of the main theorem on deformation rate.
Key words and phrases: symbolic dynamical systems, topological Markov shift, sofic system, synchronized system, magic word, invariant measure, metric entropy, Mean Ergodic theorem, boundary deformation rate.
Bibliographic databases:
Document Type: Article
MSC: 28D20, 37A05, 37A30, 37A50, 37B10.
Language: Russian
Citation: B. M. Gurevich, S. A. Komech, A. A. Tempelman, “Random averaging in ergodic theorem”, Mosc. Math. J., 19:1 (2019), 77–88
Citation in format AMSBIB
\Bibitem{GurKomTem19}
\by B.~M.~Gurevich, S.~A.~Komech, A.~A.~Tempelman
\paper Random averaging in ergodic theorem
\jour Mosc. Math.~J.
\yr 2019
\vol 19
\issue 1
\pages 77--88
\mathnet{http://mi.mathnet.ru/mmj701}
\crossref{https://doi.org/10.17323/1609-4514-2019-19-1-77-88}
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