MEAN DIMENSION THEORY IN SYMBOLIC DYNAMICS FOR FINITELY GENERATED AMENABLE GROUPS

被引：1
|
作者：
Wang, Yunping [1 ]
Chen, Ercai [2 ,3 ]
Zhou, Xiaoyao [2 ,3 ]
机构：
[1] Ningbo Univ Technol, Sch Sci, Ningbo 315211, Zhejiang, Peoples R China
[2] Nanjing Normal Univ, Sch Math Sci, Nanjing 210046, Jiangsu, Peoples R China
[3] Nanjing Normal Univ, Inst Math, Nanjing 210046, Jiangsu, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2022年 / 42卷 / 09期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Key words and phrases; Subshift; metric mean dimension; mean Hausdorff dimension; rate distortion dimension; polynomial growth group; POLYNOMIAL-GROWTH; ENTROPY;
D O I：
10.3934/dcds.2022050
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we mainly show a close relationship between topo-logical entropy and mean dimension theory for actions of polynomial growth groups. We show that metric mean dimension and mean Hausdorff dimension of subshifts with respect to the lower rank subgroup are equal to its topological entropy multiplied by the growth rate of the subgroup. Meanwhile, we prove that above result holds for rate distortion dimension of subshifts with respect to a lower rank subgroup and measure entropy. Furthermore, we present some examples.
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页码：4219 / 4236
页数：18
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