Topological speedups of ℤd-actions. Issue 2 (3rd April 2022)

• Record Type: Journal Article
• Authors: Johnson, Aimee S. A.; McClendon, David M.
• Is Part Of: Dynamical systems. Volume 37:Issue 2(2022)
• Page Start: 222
• Page End: 261
• Publication Date: 2022-04-03
• Subjects: Orbit equivalence -- minimal Cantor systems -- topological Zd-speedups -- Zd-odometers -- Kakutani-Rohklin partitions; 37B05; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2022.2033166
• Languages: English
• ISSNs: 1468-9367

Abstract

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.