Dynamical behaviour of Coven's aperiodic cellular automata

AbstractWe show that the aperiodic cellular automata studied by Coven (1980), that is the maps F : [0, 1]Z → [0, 1]Z induced by block maps f : [0, 1]r + 1 → [0, 1] such that f(x0,x1,…,xr) is equal to (x0 + 1)mod 2 if x1…xr = b1…br and equal to x0 otherwise, where B = b1…br is a given aperiodic word, have the following position in classification of K…rka (1994): they are regular, contain equicontinuous points without being equicontinuous, and are chain transitive but not topologically transitive. Therefore they do not have the shadowing property; this answers in the negative a question raised by P. K…rka