The Ellis semigroup of a nonautonomous discrete dynamical system. Issue 6 (29th September 2017)

• Record Type: Journal Article
• Authors: García-Ferreira, S.; Sanchis, M.
• Is Part Of: Quaestiones mathematicae. Volume 40:Issue 6(2017)
• Page Start: 753
• Page End: 767
• Publication Date: 2017-09-29
• Subjects: Primary 54G20 -- 54D80 -- 22A99 -- Secondary 54H11; Free ultrafilter -- discrete dynamical system -- nonautonomous discrete dynamical system -- Ellis semigroup -- compact metric space -- p-limit point; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2017.1313332
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: We introduce the Ellis semigroup of a nonautonomous discrete dynamical system ( X, f 1, ∞ ) when X is a metric compact space. The underlying set of this semigroup is the pointwise closure of in the space X X . By using the convergence of a sequence of points with respect to an ultrafilter it is possible to give a precise description of the semigroup and its operation. This notion extends the classical Ellis semigroup of a discrete dynamical system. We show several properties that connect this semigroup and the topological properties of the nonautonomous discrete dynamical system.