Ergodicity conditions on the group of 3-adic integers
Volume 147 / 2017
Colloquium Mathematicum 147 (2017), 67-75
MSC: Primary 11S82; Secondary 37P20.
DOI: 10.4064/cm6696-2-2016
Published online: 8 December 2016
Abstract
We provide necessary and sufficient conditions for ergodicity on $\mathbb {Z}_{3}$ and deduce an alternative proof for the ergodicity of 3-adic affine dynamical systems. Moreover, we prove that the ergodicity characterization by means of the van der Put series known for the group of 2-adic integers has no equivalent on $\mathbb {Z}_{3}$.
