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
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.
Received: February 21, 2003
Ya. G. Sinai, “Uniform distribution in the $(3x+1)$-problem”, Mosc. Math. J., 3:4 (2003), 1429–1440
Citation in format AMSBIB
\paper Uniform distribution in the $(3x+1)$-problem
\jour Mosc. Math.~J.
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Volkov S., “A probabilistic model for the 5x+1 problem and related maps”, Stochastic Processes and Their Applications, 116:4 (2006), 662–674
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