Abstract
Given a discrete dynamical system (X,f), we let E(X,f) denote its Ellis semigroup. We analyze the Ellis semigroup of a dynamical system having a simple k−od as phase space. We prove the following result:TheoremLet(T,f)be a discrete dynamical system where T is a simplek−odfor somek∈N. Then the following statements are equivalent:(1)The family{fn:n∈N}is not equicontinuous.(2)There existn∈Nand an arcA⊂Tsuch thatA⊊fn(A).(3)There exists a noncontinuous functiong∈E(f,X).This generalized a result of P. Szuca [10]. We provide examples for which the previous result fails for some fans. We pose some open questions related to this topic.
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