On the Interplay of Direct Topological Factorizations and Cellular Automata Dynamics on Beta-Shifts

We consider the range of possible dynamics cellular automata (CA) on two-sided beta-shifts [Formula: see text] and its relation to direct topological factorizations. show that any reversible CA has an almost equicontinuous direction whenever is not sofic. This corollary non-sofic are topologically prime, i.e. they conjugate factorizations two nontrivial subshifts text]. also give a simple criterion determine whether for given integer real when subshift finite type. When strictly sofic, we such conjugacy at least quadratic Pisot number degree conclude by using new proof classification multiplication with integral base ask exist integer.