On the Ellis semigroup of a cascade on a compact metric countable space

2018/09/17 by Quintero, Andres, Uzcategui, Carlos
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.06426

Abstract

Let X be a compact metric countable space, let f:X→ X be a homeomorphism and let E(X,f) be its Ellis semigroup. Among other results we show that the following statements are equivalent: (i) (X,f) is equicontinuous, (ii) (X,f) is distal and (iii) every point is periodic. We use this result to give a direct proof of a theorem of Ellis saying that (X,f) is distal if, and only if, E(X,f) is a group.

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