The Ellis semigroup of a nonautonomous discrete dynamical system. Issue 6 (29th September 2017) - García-Ferreira, S.; Sanchis, M.
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.