论文标题
代数系统的自然扩展的平均维度
Mean dimension of natural extension of algebraic systems
论文作者
论文摘要
进行自然延伸后，平均尺寸可能会降低。在本文中，我们表明，对于紧凑型的Abelian群体的内态性，自然扩展可以保留平均维度。作为一种应用，我们获得了代数细胞自动机的平均维度与其自然延伸的平均维度一致，从而增强了Burguet和shi \ cite {bs21}的结果，并具有不同的证明。
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 withthe mean dimension of its natural extension, which strengthens a result of Burguet and Shi \cite{BS21} with a different proof.
