Mathematics > Dynamical Systems
[Submitted on 7 Feb 2022 (v1), last revised 3 Aug 2022 (this version, v2)]
Title:Distal systems in topological dynamics and ergodic theory
View PDFAbstract: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.
Submission history
From: Henrik Kreidler [view email][v1] Mon, 7 Feb 2022 19:01:13 UTC (318 KB)
[v2] Wed, 3 Aug 2022 15:05:37 UTC (320 KB)
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