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arXiv · 1602.08380

The Ellis semigroup of a nonautonomous discrete dynamical system

S. García-Ferreira·M. Sanchis
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Abstract

We introduce the {\it Ellis semigroup} of a nonautonomous discrete dynamical system $(X,f_{1,\infty})$ when $X$ is a metric compact space. The underlying set of this semigroup is the pointwise closure of $\{f\sp{n}_1 \, |\, n\in \mathbb{N}\}$ in the space $X\sp{X}$. 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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S. García-Ferreira, M. Sanchis. 2016-02-26. The Ellis semigroup of a nonautonomous discrete dynamical system. https://arxiv.org/abs/1602.08380

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