1 results
Zero-dimensional isomorphic dynamical models
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 40 / Issue 8 / August 2020
- Published online by Cambridge University Press:
- 11 December 2018, pp. 2116-2130
- Print publication:
- August 2020
-
- Article
- Export citation
-
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 
$\unicode[STIX]{x1D6F7}$ is an aperiodic assignment on a Choquet simplex 
$K$ such that the set of extreme points 
$\mathsf{ex}K$ is a countable union 
$\bigcup _{n}E_{n}$, where each set 
$E_{n}$ is compact, zero-dimensional and the restriction of 
$\unicode[STIX]{x1D6F7}$ to the Bauer simplex 
$K_{n}$ spanned by 
$E_{n}$ can be ‘embedded’ in some topological dynamical system, then 
$\unicode[STIX]{x1D6F7}$ can be ‘realized’ in a zero-dimensional system.
