Limit measures for affine cellular automata on topological Markov subgroups

Abstract

Consider a topological Markov subgroup which is p(s)-torsion (with p prime) and an affine cellular automaton defined on it. We show that the Cesaro mean of the iterates, by the automaton of a probability measure with complete connections and summable memory decay that is compatible with the topological Markov subgroup, converges to the Haar measure.