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 Mat. Sb., 2006, Volume 197, Number 1, Pages 97–132 (Mi msb1497)

Embedding lattice actions in flows with multidimensional time

S. V. Tikhonov

Russian State University of Trade and Economics

Abstract: The genericity of the embeddability of lattice actions in flows with multidimensional time is studied. In particular, questions of de la Rue and de Sam Lazaro on the genericity of the embeddability of an action of a 2-lattice in a flow and the embeddability of a transformation in injective flow actions with multidimensional time are answered. It is also shown that a generic transformation has a set of roots of continuum cardinality in an arbitrary prescribed massive set.
Bibliography: 15 titles.

DOI: https://doi.org/10.4213/sm1497

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English version:
Sbornik: Mathematics, 2006, 197:1, 95–126

Bibliographic databases:

UDC: 517.987.5+938.5
MSC: 37A05, 37A15

Citation: S. V. Tikhonov, “Embedding lattice actions in flows with multidimensional time”, Mat. Sb., 197:1 (2006), 97–132; Sb. Math., 197:1 (2006), 95–126

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb1497
• https://doi.org/10.4213/sm1497
• http://mi.mathnet.ru/eng/msb/v197/i1/p97

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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, S. V. Tikhonov, “Typical $\mathbb Z^n$-actions can be inserted only in injective $\mathbb R^n$-actions”, Math. Notes, 79:6 (2006), 864–868
2. 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
3. S. V. Tikhonov, “A complete metric in the set of mixing transformations”, Sb. Math., 198:4 (2007), 575–596
4. V. V. Ryzhikov, “Spectral multiplicities and asymptotic operator properties of actions with invariant measure”, Sb. Math., 200:12 (2009), 1833–1845
5. Moiseev I., Sachkov Yu.L., “Maxwell strata in sub-Riemannian problem on the group of motions of a plane”, ESAIM, Control Optim. Calc. Var., 16:2 (2010), 380–399
6. Sachkov Yu.L., “Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane”, ESAIM, Control Optim. Calc. Var., 16:4 (2010), 1018–1039
7. Danilenko A.I., Ryzhikov V.V., “On self-similarities of ergodic flows”, Proc London Math Soc, 104:3 (2012), 431–454
8. Melleray J., “Extensions of Generic Measure-Preserving Actions”, Ann. Inst. Fourier, 64:2 (2014), 607–623
9. 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
10. Gao S. Hill A., “Topological isomorphism for rank-1 systems”, J. Anal. Math., 128 (2016), 1–49
11. S. V. Tikhonov, “Rigidity of Actions with Extreme Deviation from Multiple Mixing”, Math. Notes, 103:6 (2018), 977–989
12. V. V. Ryzhikov, “Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows”, Math. Notes, 104:6 (2018), 900–904
13. S. V. Tikhonov, “Multiple Mixing with Respect to Noncoinciding Sets”, Proc. Steklov Inst. Math., 308 (2020), 229–237
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