On chaotic dynamics of the minimal centre of attraction of discrete amenable group actions.

Let <italic>X</italic> be a compact metric space, <italic>G</italic> be a countable discrete infinite amenable group continuously acting on <italic>X</italic> and $ \mathcal {F} $ F be a Følner sequence of <italic>G</italic>. 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 <italic>x</italic> is not <italic>S</italic>-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, <italic>Chaotic dynamics of minimal centre of attraction of discrete amenable group actions</italic>, J. Math. Anal. Appl. 456 (2017), pp. 1397–1414.]. [ABSTRACT FROM AUTHOR]