On tameness of almost automorphic dynamical systems for general groups
Abstract
Let $(X,G)$ be a minimal equicontinuous dynamical system, where $X$ is a compact metric space and $G$ some topological group acting on $X$. Under very mild assumptions, we show that the class of regular almost automorphic extensions of $(X,G)$ contains examples of tame but nonnull systems as well as nontame ones. To do that, we first study the representation of almost automorphic systems by means of semicocycles for general groups. Based on this representation, we obtain examples of the above kind in wellstudied families of group actions. These include Toeplitz flows over $G$odometers where $G$ is countable and residually finite as well as symbolic extensions of irrational rotations.
 Publication:

arXiv eprints
 Pub Date:
 February 2019
 arXiv:
 arXiv:1902.10780
 Bibcode:
 2019arXiv190210780F
 Keywords:

 Mathematics  Dynamical Systems
 EPrint:
 doi:10.1112/blms.12304