Some Borel measures associated with the generalized Collatz mapping

Volume 63 / 1992

K. Matthews 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.

Authors

  • K. Matthews

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