Some Borel measures associated with the generalized Collatz mapping

K. Matthews

ArticleOriginal scientific text

Title

Some Borel measures associated with the generalized Collatz mapping

Authors ¹

Affiliations

Department of Mathematics, University of Queensland, St. Lucia, Brisbane 4072, Australia

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

w \hat{ℤ}

and construct finitely many ergodic Borel measures on

w \hat{ℤ}

which heuristically explain the limiting frequencies in congruence classes, observed for integer trajectories.

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Title

Some Borel measures associated with the generalized Collatz mapping

Affiliations

Abstract

Bibliography