Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658414 | Topology and its Applications | 2015 | 11 Pages |
Abstract
Given a dynamical system (X,f)(X,f), we let E(X,f)E(X,f) denote its Ellis semigroup and E(X,f)⁎=E(X,f)∖{fn:n∈N}E(X,f)⁎=E(X,f)∖{fn:n∈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)(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)⁎E(X,f)⁎ are continuous or all functions of E(X,f)⁎E(X,f)⁎ are discontinuous. We describe an example of a dynamical system (X,f)(X,f) where X is a compact metric countable space, the orbit of each accumulation point is finite and E(X,f)⁎E(X,f)⁎ contains both continuous and discontinuous functions.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
S. García-Ferreira, Y. Rodriguez-López, C. Uzcátegui,