Topological speedups of ${\mathbb{Z}}^d$-actions

Abstract

We study minimal ${\mathbb{Z}}^d$-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 ${\mathbb{Z}}^d$-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.

37 pages