Polynomial Entropy of Amenable Group Actions for Noncompact Sets

被引：0
|
作者：
Lei Liu
Xiao Yao Zhou
机构：
[1] Shangqiu Normal University,School of Mathematics and Statistics
[2] Nanjing Normal University,School of Mathematical Sciences and Institute of Mathematics
来源：
Acta Mathematica Sinica, English Series | 2023年 / 39卷
关键词：
Bowen polynomial entropy; local measure-theoretic polynomial entropy; variational principle; amenable group; 54H20; 37A35;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability measure on a compact metric space, and investigate the relation between local measure-theoretic polynomial entropy of Borel probability measures and polynomial entropy on an arbitrary subset. Also, we establish a variational principle for polynomial entropy on compact subsets in the context of amenable group actions.
引用
收藏
页码：1351 / 1368
页数：17
相关论文
共 50 条
  • [21] Topological entropy of sets of generic points for actions of amenable groups
    Dongmei Zheng
    Ercai Chen
    Science China Mathematics, 2018, 61 : 869 - 880
  • [22] Equicontinuity of minimal sets for amenable group actions on dendrites
    Shi, Enhui
    Ye, Xiangdong
    DYNAMICS: TOPOLOGY AND NUMBERS, 2020, 744 : 175 - 180
  • [23] Relative entropy dimension for countable amenable group actions
    Xiao, Zubiao
    Yin, Zhengyu
    ACTA MATHEMATICA SCIENTIA, 2023, 43 (06) : 2430 - 2448
  • [24] An Alternative Definition of Topological Entropy for Amenable Group Actions
    Wu, Haiyan
    Li, Zhiming
    JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2022, 28 (02) : 333 - 349
  • [25] RELATIVE ENTROPY DIMENSION FOR COUNTABLE AMENABLE GROUP ACTIONS
    肖祖彪
    殷正宇
    ActaMathematicaScientia, 2023, 43 (06) : 2430 - 2448
  • [26] Relative entropy dimension for countable amenable group actions
    Zubiao Xiao
    Zhengyu Yin
    Acta Mathematica Scientia, 2023, 43 : 2430 - 2448
  • [27] A variational principle of scaled entropy for amenable group actions
    Liu, Yu
    Li, Zhiming
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2025,
  • [28] An Alternative Definition of Topological Entropy for Amenable Group Actions
    Haiyan Wu
    Zhiming Li
    Journal of Dynamical and Control Systems, 2022, 28 : 333 - 349
  • [29] Bowen topological entropy of subsets for amenable group actions
    Huang, Xiaojun
    Liu, Jinsong
    Zhu, Changrong
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 472 (02) : 1678 - 1715
  • [30] THE KATOK'S ENTROPY FORMULA FOR AMENABLE GROUP ACTIONS
    Huang, Xiaojun
    Liu, Jinsong
    Zhu, Changrong
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2018, 38 (09) : 4467 - 4482
12345