S. V. Tikhonov, “Embedding lattice actions in flows with multidimensional time”, Sb. Math., 197:1 (2006), 95

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Sbornik: Mathematics, 2006, Volume 197, Issue 1, Pages 95–126
DOI: https://doi.org/10.1070/SM2006v197n01ABEH003748 (Mi sm1497)

This article is cited in 17 scientific papers (total in 17 papers)

Embedding lattice actions in flows with multidimensional time

S. V. Tikhonov

Russian State University of Trade and Economics

English version PDF (427 kB) Citations (17) Russian version article

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DOI: https://doi.org/10.1070/SM2006v197n01ABEH003748

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.

Received: 21.03.2005

Bibliographic databases:

UDC: 517.987.5+938.5

MSC: 37A05, 37A15

Language: English

Original paper language: Russian

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

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sm1497

https://doi.org/10.1070/SM2006v197n01ABEH003748

https://www.mathnet.ru/eng/sm/v197/i1/p97

This publication is cited in the following 17 articles:

Sławomir Solecki, “Generic measure preserving transformations and the closed groups they generate”, Invent. math., 231:2 (2023), 805
V. V. Ryzhikov, “Tensor simple spectrum of unitary flows”, Funct. Anal. Appl., 56:4 (2022), 327–330
Trans. Moscow Math. Soc., 82 (2021), 15–36
Anatoly Stepin, Sergey Tikhonov, Contemporary Mathematics, 772, Topology, Geometry, and Dynamics, 2021, 311
S. V. Tikhonov, “Multiple Mixing with Respect to Noncoinciding Sets”, Proc. Steklov Inst. Math., 308 (2020), 229–237
S. V. Tikhonov, “Rigidity of Actions with Extreme Deviation from Multiple Mixing”, Math. Notes, 103:6 (2018), 977–989
V. V. Ryzhikov, “Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows”, Math. Notes, 104:6 (2018), 900–904
Gao S. Hill A., “Topological isomorphism for rank-1 systems”, J. Anal. Math., 128 (2016), 1–49
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
Melleray J., “Extensions of Generic Measure-Preserving Actions”, Ann. Inst. Fourier, 64:2 (2014), 607–623
Danilenko A.I., Ryzhikov V.V., “On self-similarities of ergodic flows”, Proc London Math Soc, 104:3 (2012), 431–454
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
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
V. V. Ryzhikov, “Spectral multiplicities and asymptotic operator properties of actions with invariant measure”, Sb. Math., 200:12 (2009), 1833–1845
S. V. Tikhonov, “A complete metric in the set of mixing transformations”, Sb. Math., 198:4 (2007), 575–596
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	761
Russian version PDF:	252
English version PDF:	31
References:	113
First page:	1

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