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Trudy Moskovskogo Matematicheskogo Obshchestva, 2013, Volume 74, Issue 1, Pages 201–208 (Mi mmo544)  

This article is cited in 9 scientific papers (total in 9 papers)

Bounded ergodic constructions, disjointness, and weak limits of powers

V. V. Ryzhikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (249 kB) Citations (9)
References:
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.
Received: 28.03.2013
English version:
Transactions of the Moscow Mathematical Society, 2013, Volume 74, Pages 165–171
DOI: https://doi.org/10.1090/S0077-1554-2014-00214-4
Bibliographic databases:
Document Type: Article
UDC: 517.987
MSC: Primary 28D05; Secondary 58F11
Language: Russian
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
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\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://mathscinet.ams.org/mathscinet-getitem?mr=3235793}
\zmath{https://zbmath.org/?q=an:06371559}
\elib{https://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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960130173}
Linking options:
  • https://www.mathnet.ru/eng/mmo544
  • https://www.mathnet.ru/eng/mmo/v74/i1/p201
  • This publication is cited in the following 9 articles:
    1. DARREN CREUTZ, “Word complexity of (measure-theoretically) weakly mixing rank-one subshifts”, Ergod. Th. Dynam. Sys., 44:5 (2024), 1330  crossref
    2. Chaika J., Kra B., “A Prime System With Many Self-Joinings”, J. Mod. Dyn., 17 (2021), 213–265  crossref  mathscinet  isi  scopus
    3. V. V. Ryzhikov, “Measure-preserving rank one transformations”, Trans. Moscow Math. Soc., 81:2 (2020), 229–259  mathnet  crossref  elib
    4. V. V. Ryzhikov, “Weakly homoclinic groups of ergodic actions”, Trans. Moscow Math. Soc., 80 (2019), 83–94  mathnet  crossref  elib
    5. El Abdalaoui E.H., Shparlinski I.E., “Disjointness of the Mobius Transformation and Mobius Function”, Res. Math. Sci., 6:1 (2019), 17  crossref  mathscinet  zmath  isi  scopus
    6. 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  mathscinet  zmath  adsnasa  isi  elib
    7. 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
    8. 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
    9. 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
    Citing articles in Google Scholar: Russian citations, English citations
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    Trudy Moskovskogo Matematicheskogo Obshchestva
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