University of Oulu

Ban, J.-C., Chang, C.-H., Hu, W.-G., Lai, G.-Y., & Wu, Y.-L. (2023). An analogue of topological sequence entropy for Markov hom tree-shifts. Studia Mathematica, 270(3), 263–283.

An analogue of topological sequence entropy for Markov hom tree-shifts

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Author: Ban, Jung-Chao1; Chang, Chih-Hung2; Hu, Wen-Guei3;
Organizations: 1Department of Mathematical Sciences National Chengchi University Taipei 11605, Taiwan, ROC
2Department of Applied Mathematics National University of Kaohsiung Kaohsiung 81148, Taiwan, ROC
3College of Mathematics Sichuan University Chengdu, 610064, China
4Department of Applied Mathematics National Yang Ming Chiao Tung University Hsinchu 30010, Taiwan, ROC
5Department of Mathematical Sciences University of Oulu Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.2 MB)
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Language: English
Published: Polish Academy of Sciences, Institute of Mathematics, 2023
Publish Date: 2023-08-17


In this article, an analogue \(h^S_{\rm top}\) of topological sequence entropy is defined for Markov hom tree-shifts. We explore various aspects of \(h^S_{\rm top}\), including the existence of the limit in the definition, its relationship to topological entropy, a full characterization of null systems (with zero \(h^S_{\rm top}\) for any \(S\)), and the upper bound as well as denseness of all possible values. The relationship between this quantity and a variant called induced entropy is also breifly discussed.

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Series: Studia mathematica
ISSN: 0039-3223
ISSN-E: 1730-6337
ISSN-L: 0039-3223
Volume: 270
Issue: 3
Pages: 263 - 283
DOI: 10.4064/sm220426-13-10
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: Ban and Chang are partially supported by the Ministry of Science and Technology, ROC (Contract No MOST 109-2115-M-004-002-MY2 and 109-2115-M-390-003-MY3) and National Center for Theoretical Sciences. Hu is partially supported by the National Natural Science Foundation of China (Grant No.11601355).
Copyright information: © 2023 Instytut Matematyczny PAN. Authors retain the right to distribute their author accepted manuscript under a CC-BY license.