SOME RESULTS ON BUNDLE SYSTEMS FOR A COUNTABLE DISCRETE AMENABLE GROUP ACTION*

doi:10.1007/s10473-023-0322-1

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (3): 1382-1402.doi: 10.1007/s10473-023-0322-1

SOME RESULTS ON BUNDLE SYSTEMS FOR A COUNTABLE DISCRETE AMENABLE GROUP ACTION^*

Juan Pan¹, Yunhua Zhou^2,†

1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

收稿日期:2021-11-06 出版日期:2023-06-25 发布日期:2023-06-06
通讯作者: ^† Yunhua Zhou, E-mail: zhouyh@cqu.edu.cn
作者简介:Juan Pan, E-mail: juanpan20@hotmail.com
基金资助:
Natural Science Foundation of China (11871120, 12071082) and the Natural Science Foundation of Chongqing (cstc2021jcyj-msxmX0299).

SOME RESULTS ON BUNDLE SYSTEMS FOR A COUNTABLE DISCRETE AMENABLE GROUP ACTION^*

Juan Pan¹, Yunhua Zhou^2,†

1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received:2021-11-06 Online:2023-06-25 Published:2023-06-06
Contact: ^† Yunhua Zhou, E-mail: zhouyh@cqu.edu.cn
About author:Juan Pan, E-mail: juanpan20@hotmail.com
Supported by:
Natural Science Foundation of China (11871120, 12071082) and the Natural Science Foundation of Chongqing (cstc2021jcyj-msxmX0299).

摘要/Abstract

摘要： We consider the style number, independence number and entropy for a frame bundle dynamical system. The base system of which is a countable discrete amenable group action on a compact metric space. We obtain the existence of cover measures, an ergodic theorem about mean linear independence and the style number, and a variational principle for style numbers and independence numbers. We also study the relationship between the entropy of base systems and that of their bundle systems.

关键词: mean linear independence, style number, independence number, entropy

Abstract: We consider the style number, independence number and entropy for a frame bundle dynamical system. The base system of which is a countable discrete amenable group action on a compact metric space. We obtain the existence of cover measures, an ergodic theorem about mean linear independence and the style number, and a variational principle for style numbers and independence numbers. We also study the relationship between the entropy of base systems and that of their bundle systems.

Key words: mean linear independence, style number, independence number, entropy

Juan Pan, Yunhua Zhou. SOME RESULTS ON BUNDLE SYSTEMS FOR A COUNTABLE DISCRETE AMENABLE GROUP ACTION^*[J]. 数学物理学报(英文版), 2023, 43(3): 1382-1402.

Juan Pan, Yunhua Zhou. SOME RESULTS ON BUNDLE SYSTEMS FOR A COUNTABLE DISCRETE AMENABLE GROUP ACTION^*[J]. Acta mathematica scientia,Series B, 2023, 43(3): 1382-1402.

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SOME RESULTS ON BUNDLE SYSTEMS FOR A COUNTABLE DISCRETE AMENABLE GROUP ACTION^*

SOME RESULTS ON BUNDLE SYSTEMS FOR A COUNTABLE DISCRETE AMENABLE GROUP ACTION^*

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