AI 中文总结
研究不具标记性质的有限平均维数动力系统，证明其平均与动力学维数均为$N$，可嵌入特定立方体移位，还证得紧可度量化字母表全移位的动力学维数等于其覆盖维数。
AI 中文摘要
我们研究了前期工作中构造的非周期逆极限系统，它是一个不具有标记性质的有限平均维数动力系统实例。我们证明其平均维数与Meyerovitch动力学维数均等于$N$。尽管缺乏标记性质，该系统仍可等变拓扑嵌入到字母维数为$3N+2$的立方体移位中。作为辅助结果，我们证明了任意紧可度量化字母表上全移位的动力学维数恰好等于该字母表的覆盖维数，包括该维数为无穷的情况。
英文摘要
We study the aperiodic inverse-limit system constructed in our earlier work as an example of a finite-mean-dimensional dynamical system without the marker property. We prove that its mean dimension and Meyerovitch's dynamical dimension are both equal to $N$. Despite the absence of the marker property, the system admits an equivariant topological embedding into the cubical shift with alphabet dimension $3N+2$. As an auxiliary result, we prove that the dynamical dimension of the full shift over any compact metrizable alphabet is exactly the covering dimension of the alphabet, including when this dimension is infinite.
Comments18 pages
