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

Volume 270 / 2023

Jung-Chao Ban, Chih-Hung Chang, Wen-Guei Hu, Guan-Yu Lai, Yu-Liang Wu Studia Mathematica 270 (2023), 263-283 MSC: Primary 37B10; Secondary 37E25. DOI: 10.4064/sm220426-13-10 Published online: 12 December 2022

Abstract

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.

Authors

  • Jung-Chao BanDepartment of Mathematical Sciences
    National Chengchi University
    Taipei 11605, Taiwan, ROC
    e-mail
  • Chih-Hung ChangDepartment of Applied Mathematics
    National University of Kaohsiung
    Kaohsiung 81148, Taiwan, ROC
    e-mail
  • Wen-Guei HuCollege of Mathematics
    Sichuan University
    Chengdu, 610064, China
    e-mail
  • Guan-Yu LaiDepartment of Applied Mathematics
    National Yang Ming Chiao Tung University
    Hsinchu 30010, Taiwan, ROC
    e-mail
  • Yu-Liang WuDepartment of Mathematical Sciences
    University of Oulu
    Oulu, Finland
    e-mail

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