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Topological Speedups Of ℤD-Actions, Aimee S.A. Johnson, D. M. Mcclendon

Mathematics & Statistics Faculty Works

We study minimal 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 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. Furthermore, we give examples of speedups of ℤ^d-odometers which show the significant role played by a choice of ‘cone’ associated to the speedup.