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Specification and Shadowing Properties of Free Semigroup Actions

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Abstract

In this paper, we introduce shadowing-like properties and specification-like properties of free semigroup actions, such as periodic shadowing property, strong periodic shadowing property, special periodic shadowing property, local specification property, and local weak specification property. Furthermore, some fundamental properties of these notions are given. Finally, under some conditions, we obtain that these notions of shadowing-like properties and specification-like properties of free semigroup actions are equivalent, and the same conclusion is also obtained in the finite product systems of free semigroup actions.

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Acknowledgements

The authors really appreciate the referees’ valuable remarks and suggestions that helped a lot. Thanks to Dr. Xiaojiang Ye for his assistance in revising this paper.

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Authors and Affiliations

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

    Huihui Xu, Dongkui Ma & Yanjie Tang

  2. School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, 526061, People’s Republic of China

    Heman Fu

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  1. Huihui Xu
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  2. Dongkui Ma
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Author 1 (First Author): Theoretical derivation; writing Author 2: Ideas; formulation of overarching research goals Author 3: Participate in discussion; paper revision Author 4 (Corresponding Author): Theoretical derivation; paper revision

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Correspondence to Yanjie Tang.

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Xu, H., Ma, D., Fu, H. et al. Specification and Shadowing Properties of Free Semigroup Actions. Qual. Theory Dyn. Syst. 23, 122 (2024). https://doi.org/10.1007/s12346-024-00984-3

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