Specification and Shadowing Properties of Free Semigroup Actions

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. Furthe...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2024-07, Vol.23 (3), Article 122
Main Authors: Xu, Huihui, Ma, Dongkui, Fu, Heman, Tang, Yanjie
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Semigroups
Specifications
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Summary: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.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-024-00984-3