Mean dimension of natural extension of algebraic systems.
- Resource Type
- Article
- Authors
- Liang, Bingbing; Shi, Ruxi
- Source
- Proceedings of the American Mathematical Society. Mar2024, Vol. 152 Issue 3, p1207-1215. 9p.
- Subject
- *CELLULAR automata
*ABELIAN groups
*ENDOMORPHISMS
- Language
- ISSN
- 0002-9939
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 with the mean dimension of its natural extension, which strengthens a result of Burguet and Shi [Israel J. Math. (to appear).] with a different proof. [ABSTRACT FROM AUTHOR]