Zero-dimensional isomorphic dynamical models [article]

Tomasz Downarowicz, Lei Jin, Wolfgang Lusky, Yixiao Qiao
2018 arXiv   pre-print
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 _n E_n, where each set E_n is compact, zero-dimensional, and the restriction of Φ to the Bauer simplex K_n spanned by E_n can be 'embedded' in some topological dynamical system, then Φ can be 'realized' in a zero-dimensional system.
arXiv:1811.02206v1 fatcat:cyzo2fpcjnao5andiykngjdyza