Séminaire Logique mathématique ICJ

Gabriel Fuhrmann, "On tameness of almost automorphic dynamical systems"

Europe/Paris
112 ()

112

Description

On tameness of almost automorphic dynamical systems

Tameness is a notion which--very roughly speaking--refers to the absence of topological complexity of a dynamical system. Glasner showed that, given a minimal system with an invariant measure, tameness implies almost automorphy [1]. In a collaboration with Glasner, Jäger and Oertel, we could improve this result by showing that such a system is actually regularly almost automorphic [2].

In this talk, we complement these results by taking a closer look at tameness of regular almost automorphic systems. To that end, we briefly discuss the notion of semi-cocycle extensions which is already worth a talk in its own right.

The talk aims at giving an introduction to all of the above concepts (i.e., no prior knowledge is expected) and the basic ideas behind a joint work with Kwietniak [3].


[1] E. Glasner, The structure of tame minimal dynamical systems for general groups, Invent. Math. 211 (2018), 213-244.

[2] G. Fuhrmann, E. Glasner, T. Jäger, C. Oertel, Irregular model sets and tame dynamics, arXiv:1811.06283, (2018), 1-22.

[3] G. Fuhrmann, D. Kwietniak, On tameness of almost automorphic dynamical systems for general groups, to appear in Bull. Lon. Math. Soc. (2019).