Products and decompositions of adding machines
type: Item
instance of: scholarly article
title: Products and decompositions of adding machines
zbMATH Open document ID: 1221.37024
author: Cuijun Liu
author: Xinhe Liu
author: Jiehua Mai
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-07-18T00:00:00Z
review text: For each sequence \(k=(k_n)\) of positive integers there is an associated adding machine \(f_k\), studied here as a topological dynamical system in its natural metric. In the first part of the paper necessary and sufficient conditions are found for a countable product of adding machines \(\prod_{i\in\mathbb N}f_{k_i}\) to be topologically conjugate to an adding machine. In the second part, the question of when an adding machine decomposes into a product of adding machines, with similar results for carry systems and for rotations on \(k\)-adic topological groups. Adding machines with finite periodic orbit factors, and the structure of finite cyclic subgroups in \(k\)-adic topological groups are also studied.
reviewed by: Thomas B. Ward
Mathematics Subject Classification ID: 37B10
zbMATH DE Number: 5925554
zbMATH Keywords: carry system
zbMATH Keywords: adding machine
zbMATH Keywords: topological group
zbMATH Keywords: topological conjugacy
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.04.039
OpenAlex ID: W2126878896
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DOI: 10.1016/J.JMAA.2011.04.039
description: scientific article; zbMATH DE number 5925554