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

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Funktsional'nyi Analiz i ego Prilozheniya, 2006, Volume 40, Issue 3, Pages 85–89
DOI: https://doi.org/10.4213/faa749 (Mi faa749)

This article is cited in 23 scientific papers (total in 23 papers)

Brief communications

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

V. V. Ryzhikov^a, J.-P. Thouvenot^b

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

Full-text PDF (167 kB) Citations (23)

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

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.

Received: 17.02.2005

English version:
Functional Analysis and Its Applications, 2006, Volume 40, Issue 3, Pages 237–240
DOI: https://doi.org/10.1007/s10688-006-0038-8

Bibliographic databases:

Document Type: Article

UDC: 517.9

Language: Russian

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

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https://doi.org/10.4213/faa749

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This publication is cited in the following 23 articles:

V. V. Ryzhikov, “Self-joinings and generic extensions of ergodic systems”, Funct. Anal. Appl., 57:3 (2023), 236–247
Adam Kanigowski, Mariusz Lemańczyk, Encyclopedia of Complexity and Systems Science Series, Ergodic Theory, 2023, 109
Krzysztof Frączek, Corinna Ulcigrai, Encyclopedia of Complexity and Systems Science Series, Ergodic Theory, 2023, 333
Krzysztof Frączek, Corinna Ulcigrai, Encyclopedia of Complexity and Systems Science, 2022, 1
Trans. Moscow Math. Soc., 82 (2021), 15–36
V. V. Ryzhikov, “Measure-preserving rank one transformations”, Trans. Moscow Math. Soc., 81:2 (2020), 229–259
Adam Kanigowski, Mariusz Lemańczyk, Corinna Ulcigrai, “On disjointness properties of some parabolic flows”, Invent. math., 221:1 (2020), 1
Adam Kanigowski, Mariusz Lemańczyk, Encyclopedia of Complexity and Systems Science, 2020, 1
V. V. Ryzhikov, “Weakly homoclinic groups of ergodic actions”, Trans. Moscow Math. Soc., 80 (2019), 83–94
I. V. Klimov, V. V. Ryzhikov, “Minimal Self-Joinings of Infinite Mixing Actions of Rank 1”, Math. Notes, 102:6 (2017), 787–791
Fayad B. Kanigowski A., “Multiple Mixing For a Class of Conservative Surface Flows”, Invent. Math., 203:2 (2016), 555–614
Fraczek K. Lemanczyk M., “a Class of Mixing Special Flows Over Two Dimensional Rotations”, Discret. Contin. Dyn. Syst., 35:10 (2015), 4823–4829
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
Kulaga J., “A Note on the Isomorphism of Cartesian Products of Ergodic Flows”, J. Dyn. Control Syst., 18:2 (2012), 247–267
Kulaga-Przymus J., Parreau F., “Disjointness Properties for Cartesian Products of Weakly Mixing Systems”, Colloq. Math., 128:2 (2012), 153–177
Mariusz Lemańczyk, Mathematics of Complexity and Dynamical Systems, 2012, 1618
Lemańczyk M., Parreau F., Roy E., “Joining primeness and disjointness from infinitely divisible systems”, Proc. Amer. Math. Soc., 139:1 (2011), 185–199
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
Mariusz Lemańczyk, Encyclopedia of Complexity and Systems Science, 2009, 8554
V. V. Ryzhikov, “Self-Joinings of Commutative Actions with Invariant Measure”, Math. Notes, 83:5 (2008), 723–726

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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