MEAN DIMENSION OF NATURAL EXTENSION OF ALGEBRAIC SYSTEMS - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

MEAN DIMENSION OF NATURAL EXTENSION OF ALGEBRAIC SYSTEMS

Bingbing Liang
  • Fonction : Auteur

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)

Identifiants

  • 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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