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Mat. Zametki, 1974, Volume 16, Issue 6, Pages 981–991 (Mi mz7540)  

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

Examples of ergodic cylindrical cascades

A. B. Krygin

Moscow Power Engineering Institute

Abstract: Ergodic examples are constructed of mappings of the cylinder $S^1\times R$ of the form $Т(x,y)=(x+\alpha,y+f(x))$. Here $x\bmod1$ is a coordinate in $S^1$, $y$ is a coordinate in $R$, $\alpha$ is an irrational number, $\int_{S^1}f(x) dx=0$. Examples with continuous $f(x)$ are constructed for numbers $\alpha$ satisfying certain conditions.

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English version:
Mathematical Notes, 1974, 16:6, 1180–1186

Bibliographic databases:

UDC: 513.88
Received: 27.06.1974

Citation: A. B. Krygin, “Examples of ergodic cylindrical cascades”, Mat. Zametki, 16:6 (1974), 981–991; Math. Notes, 16:6 (1974), 1180–1186

Citation in format AMSBIB
\Bibitem{Kry74}
\by A.~B.~Krygin
\paper Examples of ergodic cylindrical cascades
\jour Mat. Zametki
\yr 1974
\vol 16
\issue 6
\pages 981--991
\mathnet{http://mi.mathnet.ru/mz7540}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=382594}
\zmath{https://zbmath.org/?q=an:0318.54042}
\transl
\jour Math. Notes
\yr 1974
\vol 16
\issue 6
\pages 1180--1186
\crossref{https://doi.org/10.1007/BF01098447}


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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. Kozlov, “Integrability and non-integrability in Hamiltonian mechanics”, Russian Math. Surveys, 38:1 (1983), 1–76  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. B. R. Fayad, M. Lemańczy, “On the ergodicity of cylindrical transformations given by the logarithm”, Mosc. Math. J., 6:4 (2006), 657–672  mathnet  crossref  mathscinet  zmath
  • Математические заметки Mathematical Notes
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