A cylinder flow arising from irregularity of distribution

K. Schmidt

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Some applications of the individual ergodic theorem to problems in number theory

Johann Cigler (1964)

Compositio Mathematica

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Some Borel measures associated with the generalized Collatz mapping

K. Matthews (1992)

Colloquium Mathematicae

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This paper is a continuation of a recent paper [2], in which the authors studied some Markov matrices arising from a mapping T:ℤ → ℤ, which generalizes the famous 3x+1 mapping of Collatz. We extended T to a mapping of the polyadic numbers $\hat{ℤ}$ and construct finitely many ergodic Borel measures on $\hat{ℤ}$ which heuristically explain the limiting frequencies in congruence classes, observed for integer trajectories.