Document Type

Article

Publication Date

2022

Published In

Dynamical Systems

Abstract

We study minimal ℤd-Cantor systems and the relationship between their speedups, their collections of invariant Borel measures, their associated unital dimension groups, and their orbit equivalence classes. In the particular case of minimal ℤd-odometers, we show that their bounded speedups must again be odometers but, contrary to the 1-dimensional case, they need not be conjugate, or even isomorphic, to the original. Furthermore, we give examples of speedups of ℤd-odometers which show the significant role played by a choice of ‘cone’ associated to the speedup.

Keywords

Orbit equivalence, minimal Cantor systems, topological ℤd-speedups, ℤd-odometers, Kakutani-Rohklin partitions

Comments

This work is a preprint that is freely available courtesy of Taylor and Francis.

Download

Included in

Mathematics Commons

Share

COinS