The systems with almost Banach mean equicontinuity for abelian group actions

Bin Zhu; Xiaojun Huang; Yuan Lian

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arXiv · 1909.00920

The systems with almost Banach mean equicontinuity for abelian group actions

Bin Zhu·Xiaojun Huang·Yuan Lian

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Abstract

In this paper, we give the concept of Banach-mean equicontinuity and prove that three concepts, Bnanach-, Weyl- and Besicovitch-mean equicontinuity of a dynamic system with abelian group action are equivalent. Furthermore, we obtain that the topological entropy of a transitive, almost Banach-mean equicontinuous dynamical system with abelain group action is zero. As an application with 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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Bin Zhu, Xiaojun Huang, Yuan Lian. 2019-09-03. The systems with almost Banach mean equicontinuity for abelian group actions. https://arxiv.org/abs/1909.00920

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