Mean dimension of continuous cellular automata

被引：3
|
作者：
Burguet, David [1 ]
Shi, Ruxi [1 ]
机构：
[1] Sorbonne Univ, Lab Probabil Stat & Modelisat, F-75005 Paris, France
来源：
ISRAEL JOURNAL OF MATHEMATICS | 2024年 / 259卷 / 01期
关键词：
ENTROPY;
D O I：
10.1007/s11856-023-2493-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) strongly permutative, permutative algebraic and unit one-dimensional automata. In higher dimensions, a CA permutative algebraic or having a spaceship has infinite mean dimension. However, building on Meyerovitch's example [Mey08], we give an example of an algebraic surjective cellular automaton with positive finite mean dimension.
引用
收藏
页码：311 / 346
页数：36
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