MEAN DIMENSION OF NATURAL EXTENSION OF ALGEBRAIC SYSTEMS
Résumé
Mean dimension may decrease after taking natural extension. In this paper we show that mean dimension stays the same after taking natural extension for an endomorphism on a compact metrizable abelian group. As an application, we obtain that the mean dimension of algebraic cellular automaton coincides with its natural extension, which strengthens a result of Burguet and Shi [1] with a different proof.
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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