Mean dimension of natural extension of algebraic systems
Abstract
Mean dimension may decrease after taking the natural extension. In this paper we show that mean dimension is preserved by natural extension for an endomorphism on a compact metrizable abelian group. As an application, we obtain that the mean dimension of an algebraic cellular automaton coincides withthe mean dimension of its natural extension, which strengthens a result of Burguet and Shi BS21 with a different proof.
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