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arXiv · 2105.03130

Directional Kronecker algebra for $\mathbb{Z}^q$-actions

Chunlin Liu·Leiye Xu
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Abstract

In this paper, directional sequence entropy and directional Kronecker algebra for $\mathbb{Z}^q$-systems are introduced. The relation between sequence entropy and directional sequence entropy are established. Meanwhile, direcitonal discrete spectrum systems and directional null systems are defined. It is shown that a $\mathbb{Z}^q$-system has directional discrete spectrum if and only if it is directional null. Moreover, it turns out that a $\mathbb{Z}^q$-system has directional discrete spectrum along $q$ linearly independent directions if and only if it has discrete spectrum.

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Chunlin Liu, Leiye Xu. 2021-05-07. Directional Kronecker algebra for $\mathbb{Z}^q$-actions. https://doi.org/10.1017/etds.2021.163

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