论文标题
鲍恩的上限平均维度有潜力
Bowen's equations for upper metric mean dimension with potential
论文作者
论文摘要
首先，我们引入了一个新的概念，称为诱导的上限平均维度具有潜在的潜力，这自然概括了上层度量平均维度的定义，而Tsukamoto的潜力对更一般的案例进行了概括，然后我们建立了其在上层和下部速率失真尺寸方面的变异原理，并在势力平均均值中均具有巨大的平均值均值和高度均值。 其次，我们继续引入两个新的概念，称为BS度量平均维度和包装BS度量均值尺寸，以建立Bowen上部度量平均值和包装上层度量尺寸的Bowen的方程，并在子集上具有潜力。此外，我们还获得了BS度量平均维度和填充BS度量平均维度的两个变异原理。 最后，还涉及对弓形措施的一组通用点的鲍恩上部度量平均维度的特殊兴趣。
Firstly, we introduce a new notion called induced upper metric mean dimension with potential, which naturally generalizes the definition of upper metric mean dimension with potential given by Tsukamoto to more general cases, then we establish variational principles for it in terms of upper and lower rate distortion dimensions and show there exists a Bowen's equation between induced upper metric mean dimension with potential and upper metric mean dimension with potential. Secondly, we continue to introduce two new notions, called BS metric mean dimension and Packing BS metric mean dimension on arbitrary subsets, to establish Bowen's equations for Bowen upper metric mean dimension and Packing upper metric mean dimension with potential on subsets. Besides, we also obtain two variational principles for BS metric mean dimension and Packing BS metric mean dimension on subsets. Finally, the special interest about the Bowen upper metric mean dimension of the set of generic points of ergodic measures are also involved.
