Abstract
Let X be a compact metric space, G be a countable discrete infinite amenable group continuously acting on X and F be a Følner sequence of G. In this paper, we acquire some ergodic properties of the discrete amenable group action ( X , G ) . By virtue of these properties, we prove the existence of syndetic sensitivity of the minimal F -centre of attraction of a point x ∈ X provided that the minimal F -centre of attraction of x is not S-generic and admits a dense set of quasi-weakly almost periodic points relative to F of ( 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.].
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