Products and decompositions of adding machines
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.
scientific article; zbMATH DE number 5925554