Dynamics of cellular automata on beta-shifts and direct topological factorizations

Abstract

We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts $S_{\beta }$. We show that any reversible CA $F:S_{\beta }\to S_{\beta }$ has an almost equicontinuous direction whenever $S_{\beta }$ is not sofic. This has the corollary that non-sofic beta-shifts are topologically direct prime. We also make some preliminary observations on direct topological factorizations of beta-shifts that are subshifts of finite type.

12 pages, 3 figures, submitted to DLT 2020