The Ellis Semigroup of Floyd-Auslander Systems

Given a topological dynamical system (X,T), where X is a compact metric space and T is a continuous self-map on X, the Ellis semigroup E(X,T) is the pointwise closure of {T^i : i ≥ 0}. In this talk, I will give a gentle introduction to the Ellis semigroup. My aim is to convince everyone of why it matters and why it’s interesting.

There is one aspect of the Ellis semigroup that doesn’t need much convincing: the fact that it is not particularly tractable. We will discuss a situation in which this is especially the case; specifically, we will talk about non-tameness. I will present a very hands-on new criterion for non-tameness obtained in [1]. If time permits, we will look at an application of this criterion in the context of so-called Floyd-Auslander systems.

In any case, the talk will be accessible and no prior knowledge of the Ellis semigroup or Floyd-Auslander systems is expected.

[1] G. Fuhrmann and C. Liu, Idempotents in the Ellis semigroup of Floyd–
Auslander systems, preprint, arXiv:2512.13341 [math.DS], 2025.