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2022 Topologically Mixing Properties of Multiplicative Integer Systems
Jung-Chao Ban, Chih-Hung Chang, Wen-Guei Hu, Guan-Yu Lai, Yu-Liang Wu
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Real Anal. Exchange 47(1): 147-166 (2022). DOI: 10.14321/realanalexch.47.1.1614278701

Abstract

Motivated from the study of multiple ergodic average, the investigation of multiplicative shift spaces has drawn much of interest among researchers. This paper focuses on the relation of topologically mixing properties between multiplicative shift spaces and traditional shift spaces. Suppose that $\mathsf{X}_\Omega^{(\ell)}$ is the multiplicative subshift derived from the shift space $\Omega$ with given $\ell > 1$. We show that $\mathsf{X}_\Omega^{(\ell)}$ is (topologically) transitive/mixing if and only if $\Omega$ is extensible/mixing. After introducing $\ell$-directional mixing property, we derive the equivalence between $\ell$-directional mixing property of $\mathsf{X}_\Omega^{(\ell)}$ and weakly mixing property of $\Omega$.

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Jung-Chao Ban. Chih-Hung Chang. Wen-Guei Hu. Guan-Yu Lai. Yu-Liang Wu. "Topologically Mixing Properties of Multiplicative Integer Systems." Real Anal. Exchange 47 (1) 147 - 166, 2022. https://doi.org/10.14321/realanalexch.47.1.1614278701

Information

Published: 2022
First available in Project Euclid: 13 June 2022

Digital Object Identifier: 10.14321/realanalexch.47.1.1614278701

Subjects:
Primary: 37B10

Keywords: multiplicative shift spaces , topologically mixing property

Rights: Copyright © 2022 Michigan State University Press

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Vol.47 • No. 1 • 2022
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