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This article is cited in 16 scientific papers (total in 16 papers)
A complete metric in the set of mixing transformations
S. V. Tikhonov
Russian State University of Trade and Economics
Abstract:
A metric in the set of mixing measure-preserving
transformations is introduced making of it a complete separable metric
space. Dense and massive subsets of this space are
investigated. A generic mixing transformation is proved to
have simple singular spectrum and to be a mixing of arbitrary
order; all its powers are disjoint. The convolution powers
of the maximal spectral type for such transformations
are mutually singular if the ratio of the corresponding exponents is
greater than 2. It is shown that the conjugates
of a generic mixing transformation are dense, as are also
the conjugates of an arbitrary fixed Cartesian product.
Bibliography: 28 titles.
DOI:
https://doi.org/10.4213/sm3743
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English version:
Sbornik: Mathematics, 2007, 198:4, 575–596
Bibliographic databases:
    
UDC:
517.938
MSC: Primary 28D05; Secondary 54E35
Received: 04.10.2006
Citation:
S. V. Tikhonov, “A complete metric in the set of mixing transformations”, Mat. Sb., 198:4 (2007), 135–158; Sb. Math., 198:4 (2007), 575–596
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/msb3743https://doi.org/10.4213/sm3743 http://mi.mathnet.ru/eng/msb/v198/i4/p135
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Tikhonov S.V., “Homogeneous spectrum and mixing transformations”, Dokl. Math., 83:1 (2011), 80–83
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Danilenko A.I., “New spectral multiplicities for mixing transformations”, Ergod. Th. Dynam. Sys., 32:2 (2012), 517–534
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S. V. Tikhonov, “Genericity of a multiple mixing”, Russian Math. Surveys, 67:4 (2012), 779–780
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S. V. Tikhonov, “Bernoulli shifts and local density property”, Moscow University Mathematics Bulletin, 67:1 (2012), 29–35
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Solomko A.V., “New spectral multiplicities for ergodic actions”, Studia Math., 208:3 (2012), 229–247
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Danilenko A.I., “A survey on spectral multiplicities of ergodic actions”, Ergod. Th. Dynam. Sys., 33:1 (2013), 81–117
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Tikhonov S.V., “Complete metric on mixing actions of general groups”, J. Dyn. Control Syst., 19:1 (2013), 17–31
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A. I. Bashtanov, “Generic Mixing Transformations Are Rank $1$”, Math. Notes, 93:2 (2013), 209–216
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I. Yaroslavtsev, “On the Asymmetry of the Past and the Future of the Ergodic $\mathbb{Z}$-Action”, Math. Notes, 95:3 (2014), 438–440
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Bashtanov A.I., “Conjugacy Classes Are Dense in the Space of Mixing a"Currency Sign (D) -Actions”, Math. Notes, 99:1-2 (2016), 9–23
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Adams T.M., Nobel A.B., “Entropy and the uniform mean ergodic theorem for a family of sets”, Trans. Am. Math. Soc., 369:1 (2017), 605–622
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Cameron J., Fang J., Mukherjee K., “Mixing and weakly mixing abelian subalgebras of type II1 factors”, J. Funct. Anal., 272:7 (2017), 2697–2725
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