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

Jung Chao Ban; Chih Hung Chang; Wen Guei Hu; Guan Yu Lai; Yu Liang Wu

doi:10.4064/sm220426-13-10

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

Jung Chao Ban
, Chih Hung Chang
, Wen Guei Hu
, Guan Yu Lai
, Yu Liang Wu

National Chengchi University
National University of Kaohsiung
Sichuan University
National Yang Ming Chiao Tung University
University of Oulu

Research output: Contribution to journal › Journal Article › peer-review

1 Scopus citations

Abstract

In this article, an analogue h^S_top of topological sequence entropy is defined for Markov hom tree-shifts. We explore various aspects of h^S_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_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.

Original language	English
Pages (from-to)	263-283
Number of pages	21
Journal	Studia Mathematica
Volume	270
Issue number	3
DOIs	https://doi.org/10.4064/sm220426-13-10
State	Published - 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2023.

Keywords

Markov hom tree-shifts
topological entropy
topological sequence entropy
topological surface entropy

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10.4064/sm220426-13-10

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author = "Ban, \{Jung Chao\} and Chang, \{Chih Hung\} and Hu, \{Wen Guei\} and Lai, \{Guan Yu\} and Wu, \{Yu Liang\}",

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doi = "10.4064/sm220426-13-10",

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AU - Ban, Jung Chao

AU - Chang, Chih Hung

AU - Hu, Wen Guei

AU - Lai, Guan Yu

AU - Wu, Yu Liang

N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2023.

PY - 2023

Y1 - 2023

N2 - In this article, an analogue hStop of topological sequence entropy is defined for Markov hom tree-shifts. We explore various aspects of hStop, including the existence of the limit in the definition, its relationship to topological entropy, a full characterization of null systems (with zero hStop 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.

AB - In this article, an analogue hStop of topological sequence entropy is defined for Markov hom tree-shifts. We explore various aspects of hStop, including the existence of the limit in the definition, its relationship to topological entropy, a full characterization of null systems (with zero hStop 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.

KW - Markov hom tree-shifts

KW - topological entropy

KW - topological sequence entropy

KW - topological surface entropy

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DO - 10.4064/sm220426-13-10

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EP - 283

JO - Studia Mathematica

JF - Studia Mathematica

IS - 3

ER -

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

Abstract

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Keywords

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