THE SYSTEMS WITH ALMOST BANACH-MEAN EQUICONTINUITY FOR ABELIAN GROUP ACTIONS

doi:10.1007/s10473-022-0307-5

Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 919-940.doi: 10.1007/s10473-022-0307-5

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THE SYSTEMS WITH ALMOST BANACH-MEAN EQUICONTINUITY FOR ABELIAN GROUP ACTIONS

Bin ZHU¹, Xiaojun HUANG^1,2, Yuan LIAN³

1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China;
2. Chongqing Key Laboratory of Analytic Mathematics and Applications, Chongqing University, Chongqing, 401331, China;
3. Department of Mathematics, Taiyuan Normal University, Jinzhong, 030619, China

Received:2020-08-20 Revised:2021-05-12 Online:2022-06-26 Published:2022-06-24
Contact: Xiaojun HUANG,E-mail:hxj@cqu.edu.cn E-mail:hxj@cqu.edu.cn
Supported by:
The second author is supported by NSF of China (11671057), NSF of Chongqing (cstc2020jcyj-msxmX0694) and the Fundamental Research Funds for the Central Universities (2018CDQYST0023).

Abstract

Abstract: In this paper, we present the concept of Banach-mean equicontinuity and prove that the Banach-, Weyl- and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent. Furthermore, we obtain that the topological entropy of a transitive, almost Banach-mean equicontinuous dynamical system of Abelian group action is zero. As an application of our main result, we show that the topological entropy of the Banach-mean equicontinuous system under the action of an Abelian groups is zero.

Key words: Abelian group action, Banach mean equicontinuous, Banach mean density, independence set

CLC Number:

37A35

Bin ZHU, Xiaojun HUANG, Yuan LIAN. THE SYSTEMS WITH ALMOST BANACH-MEAN EQUICONTINUITY FOR ABELIAN GROUP ACTIONS[J].Acta mathematica scientia,Series A, 2022, 42(3): 919-940.

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THE SYSTEMS WITH ALMOST BANACH-MEAN EQUICONTINUITY FOR ABELIAN GROUP ACTIONS

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