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Funktsional. Anal. i Prilozhen., 2006, Volume 40, Issue 3, Pages 85–89 (Mi faa749)  

This article is cited in 10 scientific papers (total in 10 papers)

Brief communications

Disjointness, Divisibility, and Quasi-Simplicity of Measure-Preserving Actions

V. V. Ryzhikova, J.-P. Thouvenotb

a M. V. Lomonosov Moscow State University
b Université Pierre & Marie Curie, Paris VI

Abstract: For weakly mixing flows, quasi-simplicity of order $2$ implies quasi-simplicity of all orders. A uniformly divisible automorphism and a $2$-quasi-simple automorphism are disjoint.

Keywords: weakly mixing flow, divisible ergodic system, quasi-simplicity, disjointness, pairwise independent joinings

DOI: https://doi.org/10.4213/faa749

Full text: PDF file (167 kB)
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English version:
Functional Analysis and Its Applications, 2006, 40:3, 237–240

Bibliographic databases:

UDC: 517.9
Received: 17.02.2005

Citation: V. V. Ryzhikov, J. Thouvenot, “Disjointness, Divisibility, and Quasi-Simplicity of Measure-Preserving Actions”, Funktsional. Anal. i Prilozhen., 40:3 (2006), 85–89; Funct. Anal. Appl., 40:3 (2006), 237–240

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Danilenko A.I., “On simplicity concepts for ergodic actions”, J. Anal. Math., 102 (2007), 77–117  crossref  mathscinet  zmath  isi  elib
    2. V. V. Ryzhikov, “Self-Joinings of Commutative Actions with Invariant Measure”, Math. Notes, 83:5 (2008), 723–726  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Frączek K., Lemańczyk M., “Ratner's property and mild mixing for special flows over two-dimensional rotations”, J. Mod. Dyn., 4:4 (2010), 609–635  mathscinet  zmath  isi
    4. Lemańczyk M., Parreau F., Roy E., “Joining primeness and disjointness from infinitely divisible systems”, Proc. Amer. Math. Soc., 139:1 (2011), 185–199  crossref  mathscinet  zmath  isi  elib  scopus
    5. Kulaga J., “A Note on the Isomorphism of Cartesian Products of Ergodic Flows”, J. Dyn. Control Syst., 18:2 (2012), 247–267  crossref  mathscinet  zmath  isi  elib  scopus
    6. Kulaga-Przymus J., Parreau F., “Disjointness Properties for Cartesian Products of Weakly Mixing Systems”, Colloq. Math., 128:2 (2012), 153–177  crossref  mathscinet  zmath  isi  elib  scopus
    7. Fraczek K. Lemanczyk M., “a Class of Mixing Special Flows Over Two Dimensional Rotations”, Discret. Contin. Dyn. Syst., 35:10 (2015), 4823–4829  crossref  mathscinet  zmath  isi  elib  scopus
    8. Kulaga-Przymus J., “on Embeddability of Automorphisms Into Measurable Flows From the Point of View of Self-Joining Properties”, Fundam. Math., 230:1 (2015), 15–76  crossref  mathscinet  zmath  isi  elib  scopus
    9. Fayad B. Kanigowski A., “Multiple Mixing For a Class of Conservative Surface Flows”, Invent. Math., 203:2 (2016), 555–614  crossref  mathscinet  zmath  isi  scopus
    10. I. V. Klimov, V. V. Ryzhikov, “Minimal Self-Joinings of Infinite Mixing Actions of Rank 1”, Math. Notes, 102:6 (2017), 787–791  mathnet  crossref  crossref  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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