About a low complexity class of Cellular Automata

Pierre Tisseur (1)

1 CMCC - Centro de Matematica, Computação e Cognição

Extending to all probability measures the notion of m-equicontinuous cellular automata introduced for Bernoulli measures by Gilman, we show that the entropy is null if m is an invariant measure and that the sequence of image measures of a shift ergodic measure by iterations of such automata converges in Cesaro mean to an invariant measure mc. Moreover this cellular automaton is still mc-equicontinuous and the set of periodic points is dense in the topological support of the measure mc. The last property is also true when m is invariant and shift ergodic.

Domaines: Systèmes dynamiques [math.DS]

Pierre Tisseur. About a low complexity class of Cellular Automata. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2008, 17-18 (346), pp.995-998. ⟨hal-00711870v2⟩