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Sbornik: Mathematics, 2007, Volume 198, Issue 4, Pages 575–596
DOI: https://doi.org/10.1070/SM2007v198n04ABEH003850 (Mi sm3743) 		 
This article is cited in 20 scientific papers (total in 20 papers)

A complete metric in the set of mixing transformations

S. V. Tikhonov

Russian State University of Trade and Economics
English version PDF (337 kB) Citations (20)
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DOI: https://doi.org/10.1070/SM2007v198n04ABEH003850
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.
Received: 04.10.2006
Russian version:
Matematicheskii Sbornik, 2007, Volume 198, Number 4, Pages 135–158
DOI: https://doi.org/10.4213/sm3743
Bibliographic databases:
UDC: 517.938
MSC: Primary 28D05; Secondary 54E35
Language: English
Original paper language: Russian
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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    Cycle of papers
    This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:816
    Russian version PDF:314
    English version PDF:17
    References:96
    First page:3
     
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