Topological speedups of ℤd-actions. Issue 2 (3rd April 2022) - Johnson, Aimee S. A.; McClendon, David M.
Abstract : 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.