Geodesic
Some Borel measures associated with the generalized Collatz mapping
Colloquium Mathematicum, Tome 63 (1992) no. 2, pp. 191-202

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DOI

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 $\widehat{ℤ}$ and construct finitely many ergodic Borel measures on $\widehat{ℤ}$ which heuristically explain the limiting frequencies in congruence classes, observed for integer trajectories. 
K. Matthews. Some Borel measures associated with the generalized Collatz mapping. Colloquium Mathematicum, Tome 63 (1992) no. 2, pp. 191-202. doi: 10.4064/cm-63-2-191-202
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