论文标题
水平集的度量平均维度的差异原理
A variational principle for the metric mean dimension of level sets
论文作者
论文摘要
我们证明了级别的上部和下度度平均维度的变异原理，\ [\ left \ {x \ in x：\ lim_ {n \ to \ infty} \ frac {1} {n} {n} {n} {n} \ sum_ = 0}电位$φ：x \ to \ mathbb r $和连续的动力学$ f：x \ to x $在紧凑的度量空间上定义并展示规范属性。该结果将上述集合的上部和下级平均值与与某些特殊措施相关的直径降低的分区理论熵的增长速率与测量熵的增长率相关。此外，我们提出了可以应用结果的几个示例。以前以拓扑熵和拓扑压力而闻名相似的结果。
We prove a variational principle for the upper and lower metric mean dimension of level sets \[ \left\{x\in X: \lim_{n\to\infty}\frac{1}{n}\sum_{j=0}^{n-1}φ(f^{j}(x))=α\right\} \] associated to continuous potentials $φ:X\to \mathbb R$ and continuous dynamics $f:X\to X$ defined on compact metric spaces and exhibiting the specification property. This result relates the upper and lower metric mean dimension of the above mentioned sets with growth rates of measure-theoretic entropy of partitions decreasing in diameter associated to some special measures. Moreover, we present several examples to which our result may be applied to. Similar results were previously known for the topological entropy and for the topological pressure.
