On chaotic dynamics of the minimal centre of attraction of discrete amenable group actions.
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| Title: | On chaotic dynamics of the minimal centre of attraction of discrete amenable group actions. |
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| Authors: | Yin, Jiandong1 (AUTHOR) jiandongyin@ncu.edu.cn, Zhou, Yating1 (AUTHOR) |
| Source: | Dynamical Systems: An International Journal. Mar2025, Vol. 40 Issue 1, p1-22. 22p. |
| Subjects: | Infinite groups, Point set theory, Compact spaces (Topology), Mathematics |
| Abstract: | Let X be a compact metric space, G be a countable discrete infinite amenable group continuously acting on X and $ \mathcal {F} $ F be a Følner sequence of G. In this paper, we acquire some ergodic properties of the discrete amenable group action $ (X, G) $ (X , G). By virtue of these properties, we prove the existence of syndetic sensitivity of the minimal $ \mathcal {F} $ F -centre of attraction of a point $ x\in X $ x ∈ X provided that the minimal $ \mathcal {F} $ F -centre of attraction of x is not S-generic and admits a dense set of quasi-weakly almost periodic points relative to $ \mathcal {F} $ F of $ (X, G) $ (X , G). The presented results enhance some main results of [Z. Chen and X. Dai, Chaotic dynamics of minimal centre of attraction of discrete amenable group actions, J. Math. Anal. Appl. 456 (2017), pp. 1397–1414.]. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | Let X be a compact metric space, G be a countable discrete infinite amenable group continuously acting on X and $ \mathcal {F} $ F be a Følner sequence of G. In this paper, we acquire some ergodic properties of the discrete amenable group action $ (X, G) $ (X , G). By virtue of these properties, we prove the existence of syndetic sensitivity of the minimal $ \mathcal {F} $ F -centre of attraction of a point $ x\in X $ x ∈ X provided that the minimal $ \mathcal {F} $ F -centre of attraction of x is not S-generic and admits a dense set of quasi-weakly almost periodic points relative to $ \mathcal {F} $ F of $ (X, G) $ (X , G). The presented results enhance some main results of [Z. Chen and X. Dai, Chaotic dynamics of minimal centre of attraction of discrete amenable group actions, J. Math. Anal. Appl. 456 (2017), pp. 1397–1414.]. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 14689367 |
| DOI: | 10.1080/14689367.2024.2410020 |
