Billingsley-Type Theorem of Weighted Bowen Topological Entropy for Amenable Group Actions

Yuan Lian () and Hongjun Liu
Additional contact information
Yuan Lian: College of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619, China
Hongjun Liu: School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China

Mathematics, 2025, vol. 13, issue 23, 1-17

Abstract: Let ( X i , d i ) be a compact metric space with metric d i , i = 1 , 2 … , k , and G be a discrete infinitely countable amenable group. This paper is based on continuous actions G ↷ X i on compact metric spaces ( X i , d i ) . Firstly, we introduce the concept of weighted Bowen balls, and then use the concept of weighted Bowen balls to introduce the corresponding lower (upper) weighted local entropy, as well as propose the concept of weighted Bowen topological entropy defined in terms of Hausdorff dimension by weighted Bowen balls, and prove Billingsley-type theorem between these two types of entropies by using the equivalent definition of weighted Bowen topological entropy.

Keywords: amenable group; weighted Bowen topological entropy; Billingsley-type theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/23/3776/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/23/3776/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:23:p:3776-:d:1802183

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().