Right-Permutative Cellular Automata on Topological Markov Chains

Abstract

In this paper we consider cellular automata $(\mathfrak{G},\Phi )$ with algebraic local rules and such that $\mathfrak{G}$ 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.

16 pages, 2 figure. A new version with improved redaction of Theorem 6.3(i)) to clearify its consequences

References in corpus (2)

• Topological Quasi-Group Shifts
• Attractiveness of the Haar measure for linear cellular automata on Markov subgroups

Cited by in corpus (2)

• Statistical Mechanics of Surjective Cellular Automata
• Standard decomposition of expansive ergodically supported dynamics