DYNAMICAL BEHAVIOR OF COVENS APERIODIC CELLULAR-AUTOMATA

We 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(x(0),x(1),...,x(r)) is equal to (x(0 ) + 1) mod 2 if x(1)...x(r) = b(1)...b(r) and equal to x(0) otherwise, where B = b(1)...b(r) is a given aperiodic word, have the following p osition in classification of Kurka (1994): they are regular, contain e quicontinuous points without being equicontinuous, and are chain trans itive but not topologically transitive. Therefore they do not have the shadowing property; this answers in the negative a question raised by P. Kurka.