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Tr. Mosk. Mat. Obs., 2013, Volume 74, Issue 1, Pages 201–208 (Mi mmo544)  
This article is cited in 4 scientific papers (total in 4 papers)

Bounded ergodic constructions, disjointness, and weak limits of powers

V. V. Ryzhikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: This paper is devoted to the disjointness property of powers of a totally ergodic bounded construction of rank 1 and some generalizations of this result. We look at applications to the problem when the Möbius function is independent of the sequence induced by a bounded construction.

Key words and phrases: ergodic power of a transformation; construction of rank one; disjointness of dynamical systems; Möbius function.

Full text: PDF file (249 kB)
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English version:
Transactions of the Moscow Mathematical Society, 2013, 74, 165–171

Bibliographic databases:

UDC: 517.987
MSC: Primary 28D05; Secondary 58F11
Received: 28.03.2013

Citation: V. V. Ryzhikov, “Bounded ergodic constructions, disjointness, and weak limits of powers”, Tr. Mosk. Mat. Obs., 74, no. 1, MCCME, M., 2013, 201–208; Trans. Moscow Math. Soc., 74 (2013), 165–171

Citation in format AMSBIB
\Bibitem{Ryz13}
\by V.~V.~Ryzhikov
\paper Bounded ergodic constructions, disjointness, and weak limits of powers
\serial Tr. Mosk. Mat. Obs.
\yr 2013
\vol 74
\issue 1
\pages 201--208
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo544}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3235793}
\zmath{https://zbmath.org/?q=an:06371559}
\elib{http://elibrary.ru/item.asp?id=21369367}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2013
\vol 74
\pages 165--171
\crossref{https://doi.org/10.1090/S0077-1554-2014-00214-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960130173}


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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. V. V. Ryzhikov, “On the Asymmetry of Multiple Asymptotic Properties of Ergodic Actions”, Math. Notes, 96:3 (2014), 416–422  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. M. S. Lobanov, V. V. Ryzhikov, “Special weak limits and simple spectrum of the tensor products of flows”, Sb. Math., 209:5 (2018), 660–671  mathnet  crossref  crossref  adsnasa  isi  elib
    3. E. H. el Abdalaoui, J. Kulaga-Przymus, M. Lemanczyk, T. de la Rue, “Mobius disjointness for models of an ergodic system and beyond”, Isr. J. Math., 228:2 (2018), 707–751  crossref  mathscinet  zmath  isi  scopus
    4. S. Ferenczi, J. Kulaga-Przymus, M. Lemanczyk, “Sarnak's conjecture: what's new”, Ergodic Theory and Dynamical Systems in Their Interactions With Arithmetics and Combinatorics, Lecture Notes in Mathematics, 2213, eds. S. Ferenczi, J. Kulaga-Przymus, M. Lemanczyk, Springer, 2018, 163–235  crossref  mathscinet  isi  scopus
    		• Trudy Moskovskogo Matematicheskogo Obshchestva
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