Article

The Ellis semigroup of a nonautonomous discrete dynamical system

Published in: Quaestiones Mathematicae
Volume 40 , issue 6 , 2017 , pages: 753–767

DOI: 10.2989/16073606.2017.1313332

Author(s): S. García-Ferreira Centro de Ciencias Matemáticas, México , M. Sanchis Institut de Matemátiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Spain

Keywords: Primary 54G20 , 54D80 , 22A99 , Secondary 54H11 , Primary 54G20 , 54D80 , 22A99 , Secondary 54H11

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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.

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