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Amenable upper mean dimensions
Analysis and Mathematical Physics ( IF 1.4 ) Pub Date : 2021-05-04 , DOI: 10.1007/s13324-021-00538-9
Zhiming Li

In this paper we formulate the notions of upper metric mean dimension and upper measure-theoretic mean dimension for amenable group actions. In particular, a different version of variational principle for amenable group actions is presented by replacing the condition on the space in Velozo and Velozo (Rate distortion theory, metric mean dimension and measure theoretic entropy. Preprint ArXiV: 1707.05762 [Math.DS], 2017) by the conditions on the systems. At last, we discuss the relation between upper metric mean dimensions and pseudo-orbits.



中文翻译:

合适的上限平均尺寸

在本文中,我们为可服从的群体行为制定了上度量平均维数和上度量理论平均维数的概念。尤其是,通过替换Velozo和Velozo中的空间条件(速率失真理论,度量平均维数和度量理论熵),提出了一种适用于群体行为的变分原理的不同版本。预印本ArXiV:1707.05762 [Math.DS],2017年),取决于系统上的条件。最后,我们讨论了度量上限平均维数与伪轨道之间的关系。

更新日期:2021-05-05
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