论文标题
围绕度量平均维度的变异原理
Around the variational principle for metric mean dimension
论文作者
论文摘要
我们研究度量平均维度的变异原理。首先，我们证明，在Lindenstrauss和Tsukamoto的各种原理中，要对千古措施采取超级措施就足够了。其次，我们得出了公制平均维度的变异原理，涉及分区的测量理论熵的生长速率降低直径，这完全具有一般性，尤其是不需要假定覆盖数量的驯服生长。所涉及的表达式是Renyi信息维度的动态版本。第三，我们为奇格 - 科赫信息维度率提供了新的表达，以实现千古转移不变的度量。最后，我们根据Brin-Katok局部熵开发了公制平均维度的下限。
We study variational principles for metric mean dimension. First we prove that in the variational principle of Lindenstrauss and Tsukamoto it suffices to take supremum over ergodic measures. Second we derive a variational principle for metric mean dimension involving growth rates of measure-theoretic entropy of partitions decreasing in diameter which holds in full generality and in particular does not necessitate the assumption of tame growth of covering numbers. The expressions involved are a dynamical version of Renyi information dimension. Third we derive a new expression for Geiger-Koch information dimension rate for ergodic shift-invariant measures. Finally we develop a lower bound for metric mean dimension in terms of Brin-Katok local entropy.
