Topologically Mixing Properties of Multiplicative Integer System

2019/11/22 by Jung‐Chao Ban, Jung-Chao Ban, Ban, Jung-Chao +10
Computer Science · Mathematics · #Cellular Automata and Applications #Mathematical Dynamics and Fractals #math.DS #msc:37B10 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1911.10000

14 pages, 6 figures

arxiv created 2019/11/22 · arxiv updated 2019/11/25

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 X_Ω^(l) is the multiplicative subshift derived from the shift space Ω with given l > 1. We show that X_Ω^(l) is (topologically) transitive/mixing if and only if Ω is extensible/mixing. After introducing l-directional mixing property, we derive the equivalence between l-directional mixing property of X_Ω^(l) and weakly mixing property of Ω.

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