Type: Article

Iterates of dynamical systems on compact metrizable countable spaces

García-Ferreira, S; Rodríguez López, Y; Uzcategui, C.;

Abstract:

Given a dynamical system (X, f), we let E(X, f) denote its Ellis semigroup and E(X, f)* = E(X, f) \ {f(n) : n is an element of N}. We analyze the Ellis semigroup of a dynamical system having a compact metric countable space as a phase space. We show that if (X, f) is a dynamical system such that X is a compact metric countable space and every accumulation point of X is periodic, then either all functions of E(X, f) * are continuous or all functions of E(X, f)* are discontinuous. We describe an example of a dynamical system (X, f) where X is a compact metric countable space, the orbit of each accumulation point is finite and E(X, f)* contains both continuous and discontinuous functions.