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Mosc. Math. J., 2003, Volume 3, Number 4, Pages 1429–1440 (Mi mmj137)  

This article is cited in 1 scientific paper (total in 1 paper)

Uniform distribution in the $(3x+1)$-problem

Ya. G. Sinaiab

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Princeton University, Department of Mathematics

Abstract: Structure theorem of the $(3x+1)$-problem claims that the images under $T^n$ of arithmetic progressions with step $2^k$ are arithmetic progressions with step $3^m$. Here $T$ is the basic underlying map and a given $3^m$ progression can be the image of many different $2^k$ progressions. This gives rise to a probability distribution on the space of $3^m$ progressions. In this paper it is shown that this distribution is in a sense close to the uniform law.

Key words and phrases: $(3x+1)$-problem, uniform distribution, characteristic function.

Full text: http://www.ams.org/.../abst3-4-2003.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 60c05
Received: February 21, 2003
Language: English

Citation: Ya. G. Sinai, “Uniform distribution in the $(3x+1)$-problem”, Mosc. Math. J., 3:4 (2003), 1429–1440

Citation in format AMSBIB
\Bibitem{Sin03}
\by Ya.~G.~Sinai
\paper Uniform distribution in the $(3x+1)$-problem
\jour Mosc. Math.~J.
\yr 2003
\vol 3
\issue 4
\pages 1429--1440
\mathnet{http://mi.mathnet.ru/mmj137}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2058805}
\zmath{https://zbmath.org/?q=an:1050.60008}


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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. Volkov S., “A probabilistic model for the 5x+1 problem and related maps”, Stochastic Processes and Their Applications, 116:4 (2006), 662–674  crossref  mathscinet  zmath  isi
  • Moscow Mathematical Journal
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