Distal systems in topological dynamics and ergodic theory
Dynamical Systems
2022-08-04 v2
Abstract
We generalize a result of Lindenstrauss on the interplay between measurable and topological dynamics which shows that every separable ergodic measurably distal dynamical system has a minimal distal model. We show that such a model can, in fact, be chosen completely canonically. The construction is performed by going through the Furstenberg--Zimmer tower of a measurably distal system and showing that at each step, there is a simple and canonical distal minimal model. This hinges on a new characterization of isometric extensions in topological dynamics.
Cite
@article{arxiv.2202.03456,
title = {Distal systems in topological dynamics and ergodic theory},
author = {Nikolai Edeko and Henrik Kreidler},
journal= {arXiv preprint arXiv:2202.03456},
year = {2022}
}