Topologically Mixing Properties of Multiplicative Integer Systems

Motivated from the study of multiple ergodic average, the investi- gation of multiplicative shift spaces has drawn much of interest among researchers. This paper focuses on the relation of topologically mix- ing properties between multiplicative shift spaces and traditional shift spaces. Suppose that X(l) is the multiplicative subshift derived from the shift space with given l > 1. We show that X(l) is (topologically) transitive/mixing if and only if is extensible/mixing.