Some Borel measures associated with the generalized Collatz mapping
Volume 63 / 1992
Colloquium Mathematicum 63 (1992), 191-202
DOI: 10.4064/cm-63-2-191-202
Abstract
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.
