Pré-Publication, Document De Travail Année : 2022

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.

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Dates et versions

hal-03907086 , version 1 (19-12-2022)

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  • HAL Id : hal-03907086 , version 1

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Bingbing Liang, Ruxi Shi. MEAN DIMENSION OF NATURAL EXTENSION OF ALGEBRAIC SYSTEMS. 2022. ⟨hal-03907086⟩
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