2018/11/06 by Downarowicz, Tomasz, Jin, Lei, Lusky, Wolfgang +1
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1811.02206
By an assignment we mean a mapping from a Choquet simplex K to probability measure-preserving systems, obeying some natural restrictions. We prove that if Φ is an aperiodic assignment on a Choquet simplex K such that the set of extreme points exK is a countable union \bigcupn En, where each set En is compact, zero-dimensional, and the restriction of Φ to the Bauer simplex Kn spanned by En can be `embedded' in some topological dynamical system, then Φ can be `realized' in a zero-dimensional system.