Some remarks on the topology of the Ellis semigroup of a discrete dynamical system (Q2850645)

In this paper the authors analyze some metric and structural properties of the Ellis semigroup \(E(X,f)\) of a dynamical system \((X,f)\), where \(X\) is a compact metric space and \(f\) is a continuous selfmap of \(X\). Their purpose is to emphasize the connection between the dynamical properties of a discrete dynamical system and the combinatorial and topological properties of the semigroup \(\beta(\mathbb{N})\). In this direction, the authors study several conditions that make the semigroup \(E(X,f)\) a compactification of \(\mathbb{N}\) with the discrete topology. They also present several metrization theorems of the Ellis semigroup related to equicontinuity. In another result the authors show that, for topologically transitive dynamical systems, the semigroup \(E(X,f)\) is a topological semigroup if and only if it is metrizable with the supremum metric.