V. I. Oseledets, “An automorphism with simple, continuous spectrum not having the group property”, Mat. Zametki, 5:3 (1969), 323–326; Math. Notes, 5:3 (1969), 196

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Matematicheskie Zametki, 1969, Volume 5, Issue 3, Pages 323–326 (Mi mzm6851)

This article is cited in 14 scientific papers (total in 14 papers)

An automorphism with simple, continuous spectrum not having the group property

V. I. Oseledets

Full-text PDF (287 kB) Citations (14)

Abstract: An example is constructed of an automorphism with simple and continuous spectrum which does not have the group property.

Received: 11.06.1968

English version:
Mathematical Notes, 1969, Volume 5, Issue 3, Pages 196–198
DOI: https://doi.org/10.1007/BF01388626

Bibliographic databases:

UDC: 517.9

Language: Russian

Citation: V. I. Oseledets, “An automorphism with simple, continuous spectrum not having the group property”, Mat. Zametki, 5:3 (1969), 323–326; Math. Notes, 5:3 (1969), 196–198

Citation in format AMSBIB

\Bibitem{Ose69}

\by V.~I.~Oseledets

\paper An~automorphism with simple, continuous spectrum not having the group property

\jour Mat. Zametki

\yr 1969

\vol 5

\issue 3

\pages 323--326

\mathnet{http://mi.mathnet.ru/mzm6851}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=257323}

\zmath{https://zbmath.org/?q=an:0181.13902|0176.44603}

\transl

\jour Math. Notes

\yr 1969

\vol 5

\issue 3

\pages 196--198

\crossref{https://doi.org/10.1007/BF01388626}

Linking options:

https://www.mathnet.ru/eng/mzm6851

https://www.mathnet.ru/eng/mzm/v5/i3/p323

This publication is cited in the following 14 articles:

V. V. Ryzhikov, “Zhestkie puassonovskie nadstroiki bez kornei”, Matem. zametki, 117:1 (2025), 146–150
V. V. Ryzhikov, “Kolmogorov and Rokhlin spectral problems in the class of mixing automorphisms”, Russian Math. Surveys, 79:6 (2024), 1093–1094
V. V. Ryzhikov, “Mixing Sets for Rigid Transformations”, Math. Notes, 110:4 (2021), 565–570
V. V. Ryzhikov, “Compact families and typical entropy invariants of measure-preserving actions”, Trans. Moscow Math. Soc., 82 (2021), 117–123
V. V. Ryzhikov, “Measure-preserving rank one transformations”, Trans. Moscow Math. Soc., 81:2 (2020), 229–259
V. V. Ryzhikov, “Weak Closure of Infinite Actions of Rank 1, Joinings, and Spectrum”, Math. Notes, 106:6 (2019), 957–965
M. S. Lobanov, V. V. Ryzhikov, “Special weak limits and simple spectrum of the tensor products of flows”, Sb. Math., 209:5 (2018), 660–671
V. V. Ryzhikov, A. E. Troitskaya, “Mixing flows with homogeneous spectrum of multiplicity $2$”, J. Math. Sci., 248:5 (2020), 642–646
A. A. Prikhod'ko, “Ergodic Automorphisms with Simple Spectrum and Rapidly Decreasing Correlations”, Math. Notes, 94:6 (2013), 968–973
V. V. Ryzhikov, “Weak limits of powers, simple spectrum of symmetric products, and rank-one mixing constructions”, Sb. Math., 198:5 (2007), 733–754
V. V. Ryzhikov, “On the Ranks of an Ergodic Automorphism $T\times T$”, Funct. Anal. Appl., 35:2 (2001), 151–153
V. V. Ryzhikov, “Intertwinings of tensor products, and the stochastic centralizer of dynamical systems”, Sb. Math., 188:2 (1997), 237–263
V. V. Ryzhikov, “The isomorphism of measure-preserving transformations with isomorphic Cartesian powers is typical”, Math. Notes, 59:4 (1996), 453–456
A. M. Stepin, “Spectral properties of generic dynamical systems”, Math. USSR-Izv., 29:1 (1987), 159–192

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

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