Geodesic
Self-joinings and generic extensions of ergodic systems
Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 3, pp. 74-88.

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It is proved that the generic extensions of a dynamical system inherit the triviality of pairwise independent self-joinings. This property is related to well-known problems of joining theory and to Rokhlin's famous multiple mixing problem.
Keywords: pairwise independent joinings, local rigidity of cocycles, generic extensions of actions, relative multiple mixing. 
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V. V. Ryzhikov. Self-joinings and generic extensions of ergodic systems. Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 3, pp. 74-88. http://geodesic.mathdoc.fr/item/FAA_2023_57_3_a3/

[1] E. Glasner, J.-P. Thouvenot, B. Weiss, “On some generic classes of ergodic measure preserving transformations”, Tr. MMO, 82:1 (2021), 19–44 | MR | Zbl

[2] V. V. Ryzhikov, Generic extensions of ergodic actions, arXiv: 2209.09160

[3] T. Austin, E. Glasner, J.-P. Thouvenot, B. Weiss, “An ergodic system is dominant exactly when it has positive entropy”, Ergodic Theory Dynam. Systems (to appear)

[4] A. del Junco, D. Rudolph, “On ergodic action whose self-joinings are graphs”, Ergodic Theory Dynam. Systems, 7 (1987), 531–557 | DOI | MR | Zbl

[5] V. V. Ryzhikov, “Spleteniya tenzornykh proizvedenii i stokhasticheskii tsentralizator dinamicheskikh sistem”, Matem. sb., 188:2 (1997), 67–94 | DOI | MR | Zbl

[6] B. Fayad, A. Kanigowski, “Multiple mixing for a class of conservative surface flows”, Invent. Math., 203:2 (2016), 555–614 | DOI | MR | Zbl

[7] V. V. Ryzhikov, Zh.-P. Tuveno, “Diz'yunktnost, delimost i kvaziprostota sokhranyayuschikh meru deistvii”, Funkts. analiz i ego pril., 40:3 (2006), 85–89 | DOI | MR | Zbl

[8] V. V. Ryzhikov, “Polimorfizmy, dzhoiningi i tenzornaya prostota dinamicheskikh sistem”, Funkts. analiz i ego pril., 31:2 (1997), 45–57 | DOI | MR | Zbl

[9] M. Lemańczyk, F. Parreau, “Rokhlin extensions and lifting disjointness”, Ergodic Theory Dynam. Systems, 23:5 (2003), 1525–1550 | DOI | MR | Zbl

[10] M. E. Lipatov, “Klassifikatsiya kotsiklov nad ergodicheskimi avtomorfizmami so znacheniyami v gruppe Lorentsa. Rekurrentnost kotsiklov”, Matem. zametki, 93:6 (2013), 869–877 | DOI | Zbl

[11] J. King, “Ergodic properties where order $4$ implies infinite order”, Israel J. Math., 80:1–2 (1992), 65–86 | DOI | MR | Zbl

[12] V. V. Ryzhikov, “Dzhoiningi, spleteniya, faktory i peremeshivayuschie svoistva dinamicheskikh sistem”, Izv. RAN. Ser. matem., 57:1 (1993), 102–128 | Zbl

[13] S. V. Tikhonov, “O narushenii kratnogo peremeshivaniya, blizkom k ekstremalnomu”, Tr. MMO, 82:1 (2021), 205–215 | Zbl

[14] V. V. Ryzhikov, “Chetnaya i nechetnaya prostota dinamicheskikh sistem s invariantnoi meroi”, Matem. zametki, 60:3 (1996), 470–473 | DOI | MR | Zbl

[15] E. Glasner, B. Weiss, “Relative weak mixing is generic”, Sci. China Math., 62:1 (2019), 69–72 | DOI | MR | Zbl

[16] A. M. Vershik, “Polymorphisms, Markov processes, and quasi-similarity”, Discrete Contin. Dyn. Syst., 13:5 (2005), 1305–1324 | DOI | MR | Zbl