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

This article is cited in 12 scientific papers (total in 12 papers)

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

Full text: PDF file (715 kB)
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English version:
Sbornik: Mathematics, 2006, 197:1, 95–126

Bibliographic databases:

UDC: 517.987.5+938.5
MSC: 37A05, 37A15
Received: 21.03.2005

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

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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. S. V. Tikhonov, “A complete metric in the set of mixing transformations”, Sb. Math., 198:4 (2007), 575–596  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. V. V. Ryzhikov, “Spectral multiplicities and asymptotic operator properties of actions with invariant measure”, Sb. Math., 200:12 (2009), 1833–1845  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    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  crossref  mathscinet  zmath  isi  elib  scopus
    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  crossref  mathscinet  zmath  isi  elib  scopus
    7. Danilenko A.I., Ryzhikov V.V., “On self-similarities of ergodic flows”, Proc London Math Soc, 104:3 (2012), 431–454  crossref  mathscinet  zmath  isi  elib  scopus
    8. Melleray J., “Extensions of Generic Measure-Preserving Actions”, Ann. Inst. Fourier, 64:2 (2014), 607–623  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  zmath  isi  elib  scopus
    10. Gao S. Hill A., “Topological isomorphism for rank-1 systems”, J. Anal. Math., 128 (2016), 1–49  crossref  mathscinet  zmath  isi  scopus
    11. S. V. Tikhonov, “Rigidity of Actions with Extreme Deviation from Multiple Mixing”, Math. Notes, 103:6 (2018), 977–989  mathnet  crossref  crossref  isi  elib
    12. V. V. Ryzhikov, “Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows”, Math. Notes, 104:6 (2018), 900–904  mathnet  crossref  crossref  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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