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This article is cited in 6 scientific papers (total in 6 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.
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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
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\transl
\jour Trans. Moscow Math. Soc.
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http://mi.mathnet.ru/eng/mmo544 http://mi.mathnet.ru/eng/mmo/v74/i1/p201
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This publication is cited in the following articles:
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V. V. Ryzhikov, “On the Asymmetry of Multiple Asymptotic Properties of Ergodic Actions”, Math. Notes, 96:3 (2014), 416–422
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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
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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
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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
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V. V. Ryzhikov, “Weakly homoclinic groups of ergodic actions”, Trans. Moscow Math. Soc., 80 (2019), 83–94
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El Abdalaoui E.H., Shparlinski I.E., “Disjointness of the Mobius Transformation and Mobius Function”, Res. Math. Sci., 6:1 (2019), 17
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