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

Abstract

<p>We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts S β Sβ. We show that any reversible CA F:S β →S β F:Sβ→Sβ

has an almost equicontinuous direction whenever S β Sβ is not sofic. This has the corollary that non-sofic beta-shifts are topologically direct prime, i.e. they are not conjugate to direct topological factorizations X×Y X×Y

of two nontrivial subshifts <em>X</em> and <em>Y</em>. We also make some preliminary observations on direct topological factorizations of beta-shifts that are subshifts of finite type.<br /></p>