Directional weak mixing for $\mathbb{Z}^q$-actions

Chunlin Liu

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arXiv · 2106.07950

Directional weak mixing for $\mathbb{Z}^q$-actions

Chunlin Liu

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Abstract

In this paper, we introduce and characterize the concept of directional weak mixing through independence, sequence entropy, the mean ergodic theorem, and other notions. Additionally, we deduce a directional version of the Koopman-von Neumann spectrum mixing theorem. Furthermore, we explore the relation between directional weak mixing and weak mixing.

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Chunlin Liu. 2021-06-15. Directional weak mixing for $\mathbb{Z}^q$-actions. https://arxiv.org/abs/2106.07950

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