The Systems with Almost Banach-Mean Equicontinuity for Abelian Group Actions
Acta Mathematica Scientia(2022)
Abstract
In this paper, we present the concept of Banach-mean equicontinuity and prove that the Banach-, Weyl- and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent. Furthermore, we obtain that the topological entropy of a transitive, almost Banach-mean equicontinuous dynamical system of Abelian group action is zero. As an application of our main result, we show that the topological entropy of the Banach-mean equicontinuous system under the action of an Abelian groups is zero.
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Key words
Abelian group action,Banach mean equicontinuous,Banach mean density,independence set
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