Right-permutative cellular automata on topological Markov chains

Abstract

In this paper we consider cellular automata (ℜ, Φ) with algebraic local rules and such that ℜ is a topological Markov chain which has a structure compatible to this local rule. We characterize such cellular automata and study the convergence of the Cesàro mean distribution of the iterates of any probability measure with complete connections and summable decay.