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arXiv · 2103.02012

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

Aimee S. A. Johnson·David M. McClendon
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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.

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Aimee S. A. Johnson, David M. McClendon. 2021-03-02. Topological speedups of $\mathbb{Z}^d$-actions. https://arxiv.org/abs/2103.02012

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