Some properties of cellular automata with equicontinuity points

François Blanchard (1) , Pierre Tisseur (1)

1 IML - Institut de mathématiques de Luminy

We investigate topological and ergodic properties of cellular automata having equicontinuity points. In this class surjectivity on a transitive SFT implies existence of a dense set of periodic points.Our main result is that under the action of such an automaton any shift ergodic measure converges in Cesaro Mean.

Mots clés: cellular automata; Invariant measure; Cesaro mean

Domaines: Systèmes dynamiques [math.DS]; Dynamique Chaotique [nlin.CD]

François Blanchard, Pierre Tisseur. Some properties of cellular automata with equicontinuity points. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2000, 36, pp.569-582. ⟨hal-00000924⟩