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The Upper Capacity Topological Entropy of Free Semigroup Actions for Certain Non-compact Sets, II

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Abstract

This paper’s major purpose is to continue the work of Zhu and Ma in [J Stat Phys 182(1):19, 2021]. To begin, the \({\textbf{g}}\)-almost product property, more general irregular and regular sets, and some new notions of the Banach upper density recurrent points and transitive points of free semigroup actions are introduced. Furthermore, under the \({\textbf{g}}\)-almost product property and other conditions, we coordinate the Banach upper recurrence, transitivity with (ir)regularity, and obtain lots of generalized multifractal analyses for general observable functions of free semigroup actions. Finally, statistical \(\omega \)-limit sets are used to consider the upper capacity topological entropy of the sets of Banach upper recurrent points and transitive points of free semigroup actions, respectively. Our analysis generalizes the results obtained by Huang et al. in [Nonlinearity 32(7):2721–2757, 2019] and Pfister and Sullivan in [Ergodic Theory Dynam Syst 27(3):929–956, 2007].

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Acknowledgements

The authors really appreciate the referees’ valuable remarks and suggestions that helped a lot.

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Authors and Affiliations

  1. School of Mathematics, South China University of Technology, Guangzhou, 510641, People’s Republic of China

    Yanjie Tang, Xiaojiang Ye & Dongkui Ma

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  1. Yanjie Tang
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  2. Xiaojiang Ye
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  3. Dongkui Ma
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Correspondence to Dongkui Ma.

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Communicated by Marco Lenci.

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Tang, Y., Ye, X. & Ma, D. The Upper Capacity Topological Entropy of Free Semigroup Actions for Certain Non-compact Sets, II. J Stat Phys 190, 75 (2023). https://doi.org/10.1007/s10955-023-03083-w

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