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Mat. Zametki, 2006, Volume 79, Issue 6, Pages 925–930 (Mi mz2765)  

This article is cited in 2 scientific papers (total in 2 papers)

Typical $\mathbb Z^n$-actions can be inserted only in injective $\mathbb R^n$-actions

V. V. Ryzhikova, S. V. Tikhonovb

a M. V. Lomonosov Moscow State University
b Russian State University of Trade and Economics

Abstract: 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.

DOI: https://doi.org/10.4213/mzm2765

Full text: PDF file (227 kB)
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English version:
Mathematical Notes, 2006, 79:6, 864–868

Bibliographic databases:

UDC: 517.987.5+938.5
Received: 17.11.2005

Citation: V. V. Ryzhikov, S. V. Tikhonov, “Typical $\mathbb Z^n$-actions can be inserted only in injective $\mathbb R^n$-actions”, Mat. Zametki, 79:6 (2006), 925–930; Math. Notes, 79:6 (2006), 864–868

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. V. V. Ryzhikov, “Factors, rank, and embedding of a generic $\mathbb Z^n$-action in an $\mathbb R^n$-flow”, Russian Math. Surveys, 61:4 (2006), 786–787  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. 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
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