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Distal systems in topological dynamics and ergodic theory

Part of: Ergodic theory Topological dynamics

Published online by Cambridge University Press:  01 August 2022

NIKOLAI EDEKO Open the ORCID record for NIKOLAI EDEKO [Opens in a new window]  and
HENRIK KREIDLER Open the ORCID record for HENRIK KREIDLER [Opens in a new window]
NIKOLAI EDEKO
Affiliation:
Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland (e-mail: nikolai.edeko@math.uzh.ch)
HENRIK KREIDLER*
Affiliation:
Fachgruppe für Mathematik und Informatik, Bergische Universität Wuppertal, Gaußstraße 20, D-42119 Wuppertal, Germany
*
e-mail: kreidler@uni-wuppertal.de
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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.

Keywords

ergodic theorytopological dynamicsdistal systemstopological models

MSC classification

Primary: 37A05: Measure-preserving transformations 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 8 , August 2023 , pp. 2651 - 2672
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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