Directional Entropy and Pinsker $\sigma $-Algebra for $\mathbb {Z}^{2}$-Actions

Abstract

In this paper, we study the directional entropy along irrational directions in $\mathbb {R}^2$ and present the structure of directional Pinsker $\sigma $-algebra of $\mathbb {Z}^2$-MPSs.

Keywords

$\sigma $-algebra')">Directional Pinsker $\sigma $-algebra / Directional entropy

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Funding

National Natural Science Foundation of China(12031019)

Fundamental Research Funds for the Central Universities(2020kfyXJJS036)