Typical $\mathbb Z^n$-actions can be inserted only in injective $\mathbb R^n$-actions
Matematičeskie zametki, Tome 79 (2006) no. 6, pp. 925-930
Cet article a éte moissonné depuis la source Math-Net.Ru
We study actions of the groups $\mathbb Z^n$ and $\mathbb R^n$ by Lebesgue space automorphisms. We prove that a typical $\mathbb Z^n$-action can be inserted only in injective actions of $\mathbb R^n$, $n\in\mathbb N$. We give a simple proof of the fact that a typical $\mathbb Z^2$-action cannot be inserted in an $\mathbb R$-action.
@article{MZM_2006_79_6_a9,
author = {V. V. Ryzhikov and S. V. Tikhonov},
title = {Typical $\mathbb Z^n$-actions can be inserted only in injective $\mathbb R^n$-actions},
journal = {Matemati\v{c}eskie zametki},
pages = {925--930},
year = {2006},
volume = {79},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_6_a9/}
}
TY - JOUR AU - V. V. Ryzhikov AU - S. V. Tikhonov TI - Typical $\mathbb Z^n$-actions can be inserted only in injective $\mathbb R^n$-actions JO - Matematičeskie zametki PY - 2006 SP - 925 EP - 930 VL - 79 IS - 6 UR - http://geodesic.mathdoc.fr/item/MZM_2006_79_6_a9/ LA - ru ID - MZM_2006_79_6_a9 ER -
V. V. Ryzhikov; S. V. Tikhonov. Typical $\mathbb Z^n$-actions can be inserted only in injective $\mathbb R^n$-actions. Matematičeskie zametki, Tome 79 (2006) no. 6, pp. 925-930. http://geodesic.mathdoc.fr/item/MZM_2006_79_6_a9/
[1] Kuratovskii K., Topologiya, T. 1, Mir, M., 1966
[2] Glasner E., King J. L., “A zero-one law for dynamical properties”, Contemp. Math., 215 (1998), 231–242 | MR | Zbl
[3] de la Rue T., se Sam Lasaro J., “Une transformation générique peut être insérée dans un flot”, Ann. Inst. H. Poincaré Probab. Statist., 39:1 (2003), 121–134 | DOI | MR | Zbl
[4] Stepin A. M., Eremenko A., “Tipichnoe sokhranyayuschee meru preobrazovanie imeet obshirnyi tsentralizator”, Dokl. RAN, 394:6 (2004), 739–742 | MR
[5] Rokhlin V. A., “Izbrannye voprosy metricheskoi teorii dinamicheskikh sistem”, UMN, 30:2 (1949), 57–128 | Zbl
[6] Tikhonov S. V., “Vlozheniya deistvii reshetki v potoki s mnogomernym vremenem”, Matem. sb., 197:1 (2006), 97–132 | MR