论文标题
一些关于度量平均维度变分原理的注释
Some notes on variational principle for metric mean dimension
论文作者
论文摘要
首先，我们回答了古特曼（Gutman）问的问题1和$ \ rm \ acute {\ s} $ piewak in \ cite {gs20}，然后我们建立了一个双重变量原理，用于r $ \ bar {e} $ nyi信息dimension的平均维度，并显示$ \ lims $ \ lim $ \ lims的顺序（或$ \ lims）（或）在Marker属性下，可以更改按R $ \ bar {e} $ NYI信息维度和$ \ rm \ actute {\ s} $ piewak获得的公制平均维度。最后，我们尝试介绍最大度量平均维度度量的概念，这是该概念的类似物，称为经典最大熵措施与拓扑熵有关。
Firstly, we answer the problem 1 asked by Gutman and $\rm \acute{\ S}$piewak in \cite{gs20}, then we establish a double variational principle for mean dimension in terms of R$\bar{e}$nyi information dimension and show the order of $\sup$ and $\limsup$ (or $\liminf$) of the variational principle for the metric mean dimension in terms of R$\bar{e}$nyi information dimension obtained by Gutman and $\rm \acute{\ S}$piewak can be changed under the marker property. Finally, we attempt to introduce the notion of maximal metric mean dimension measure, which is an analogue of the concept called classical maximal entropy measure related to the topological entropy.
