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Weak closures of ergodic actions. (English. Russian original) Zbl 1373.37010

Math. Notes 101, No. 2, 277-283 (2017); translation from Mat. Zametki 100, No. 6, 847-854 (2016).
Summary: In the paper, the semigroup of weak limits of the powers of an infinite transformation of rank one of Chacon type is completely described.

MSC:

37A25 Ergodicity, mixing, rates of mixing
28D05 Measure-preserving transformations
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References:

[1] A. M. Stepin, “Spectral properties of generic dynamical systems,” Izv. Akad. Nauk SSSR Ser. Mat. 50 (4), 801-834 (1986) [Math. USSR-Izv. 29, 159-192 (1987)]. · Zbl 0631.28013
[2] A. I. Danilenko and V. V. Ryzhikov, “Spectral multiplicities of infinite measure preserving transformations,” Funktsional. Anal. Prilozhen. 44 (3), 1-13 (2010) [Functional Anal. Appl. 44 (3), 161-170 (2010)]. · Zbl 1271.28013 · doi:10.4213/faa3003
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[7] V. V. Ryzhikov, Weak Closure Theorem for Double Staircase Actions, arXiv: 1108. 0568.
[8] E. Janvresse, A. A. Prikhod’ko, T. de la Rue, and V. V. Ryzhikov, “Weak limits of powers of Chacon’s automorphism,” Ergodic Theory Dynam. Systems 35 (1), 128-141 (2015). · Zbl 1351.37004 · doi:10.1017/etds.2013.49
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