About: We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts [Formula: see text]. We show that any reversible CA [Formula: see text] has an almost equicontinuous direction whenever [Formula: see text] 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 [Formula: see text] of two nontrivial subshifts X and Y. We also make some preliminary observations on direct topological factorizations of beta-shifts that are subshifts of finite type.   Goto Sponge  NotDistinct  Permalink

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  • We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts [Formula: see text]. We show that any reversible CA [Formula: see text] has an almost equicontinuous direction whenever [Formula: see text] 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 [Formula: see text] of two nontrivial subshifts X and Y. We also make some preliminary observations on direct topological factorizations of beta-shifts that are subshifts of finite type.
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  • Mathematical analysis
  • Computational fields of study
  • Systems theory
  • Automata (computation)
  • Dynamical systems
  • Cellular automata
  • Symbolic dynamics
  • Combinatorics on words
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