Iterates of dynamical systems on compact metrizable countable spaces

作者：Garcia Ferreira S; Rodriguez Lopez Y; Uzcategui C^*

来源：Topology and Its Applications, 2015, 180: 100-110.

DOI：10.1016/j.topol.2014.11.007

• Discrete dynamical system
• Compact metric countable space
• p-Iterate
• p-Limit point
• Ellis semigroup

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.

• 出版日期2015-2-1