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 Sβ. We show that any reversible CA F:Sβ Sβ has an almost equicontinuous direction whenever Sβ 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.
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