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

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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 $\widehat{ℤ}$ and construct finitely many ergodic Borel measures on $\widehat{ℤ}$ which heuristically explain the limiting frequencies in congruence classes, observed for integer trajectories.
DOI : 10.4064/cm-63-2-191-202

K. Matthews 1

1 
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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. http://geodesic.mathdoc.fr/articles/10.4064/cm-63-2-191-202/

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