Geodesic
Rigidity of Actions with Extreme Deviation from Multiple Mixing
Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 912-926.

Voir la notice de l'article provenant de la source Math-Net.Ru

We introduce a class of systems, including Ledrappier's example, which do not have multiple mixing. A classification of such systems for 2D lattice actions is constructed.
Keywords: measure-preserving transformation, dynamical system, multiple mixing, Ledrappier's example. 
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S. V. Tikhonov. Rigidity of Actions with Extreme Deviation from Multiple Mixing. Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 912-926. http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a9/

[1] V. V. Ryzhikov, “Peremeshivanie, rang i minimalnoe samoprisoedinenie deistvii s invariantnoi meroi”, Matem. sb., 183:3 (1992), 133–160 | MR | Zbl

[2] V. A. Rokhlin, “Ob endomorfizmakh kompaktnykh kommutativnykh grupp”, Izv. AN SSSR. Ser. matem., 13:4 (1949), 329–340 | MR | Zbl

[3] F. Ledrappier, “Un champ markovien peut etre d'entropie nulle et melangeant”, C. R. Acad. Sci. Paris Sér. A, 287:7 (1978), 561–563 | MR | Zbl

[4] K. Schmidt, “Dynamical properties of principal algebraic group actions”, Ergodic Theory and Dynamical Systems: Perspectives and Prospects, 2012 https://warwick.ac.uk/fac/sci/maths/research/events/2010-2011/symposium1011/etdspp/schedule/schmidt.pdf

[5] S. V. Tikhonov, “Ob otsutstvii kratnogo peremeshivaniya i tsentralizatore sokhranyayuschikh meru deistvii”, Matem. zametki, 97:4 (2015), 636–640 | DOI | MR | Zbl

[6] Th. de La Rue, J. de Sam Lazaro, “Une transformation générique peut être insérée dans un flot”, Ann. Inst. H. Poincaré Probab. Statist., 39:1 (2003), 121–134 | MR | Zbl

[7] A. M. Stepin, A. M. Eremenko, “Tipichnoe sokhranyayuschee meru preobrazovanie imeet obshirnyi tsentralizator”, Dokl. AN, 394:6 (2004), 739–742 | MR | Zbl

[8] S. V. Tikhonov, “Tipichnoe deistvie gruppy $\mathbb{Z}^{d}$ vkladyvaetsya v deistvie gruppy $\mathbb{R}^{d}$”, Dokl. AN, 391:1 (2003), 26–28 | MR | Zbl

[9] S. V. Tikhonov, “Vlozheniya deistvii reshetki v potoki s mnogomernym vremenem”, Matem. sb., 197:1 (2006), 97–132 | DOI | MR | Zbl

[10] D. Koks, Dzh. Littl, D. O'Shi, Idealy, mnogoobraziya i algoritmy. Vvedenie v vychislitelnye aspekty algebraicheskoi geometrii i kommutativnoi algebry, Mir, M., 2000 | MR | Zbl

[11] T. Ward, “Three results on mixing shapes”, New York J. Math., 3A (1997), 1–10 | MR | Zbl

[12] M. Einsiedler, T. Ward, “Entropy geometry and disjointness for zero-dimensional algebraic actions”, J. Reine Angew. Math., 584 (2005), 195–214 | DOI | MR | Zbl

[13] V. V. Ryzhikov, “Ob asimmetrii kratnykh asimptoticheskikh svoistv ergodicheskikh deistvii”, Matem. zametki, 96:3 (2014), 432–439 | DOI | MR | Zbl

[14] K. Schmidt, Dynamical Systems of Algebraic Origin, Progr. Math., 128, Birkhäuser Verlag, Basel, 1995 | MR