The generic limit set of cellular automata

Saliha Djenaoui (1) , Pierre Guillon (2)

1 UBMA - Université Badji Mokhtar [Annaba]
2 I2M - Institut de Mathématiques de Marseille

In this article, we consider a topological dynamical system. The generic limit set is the smallest closed subset which has a comeager realm of attraction. We study some of its topological properties, and the links with equicontinuity and sensitivity. We emphasize the case of cellular automata, for which the generic limit set is included in all subshift attractors, and discuss directional dynamics, as well as the link with measure-theoretical similar notions.

Mots clés: attractor; directional dynamics; limit set; Baire category; symbolic dynamics; cellular automata; basin of attraction

Domaines: Systèmes dynamiques [math.DS]

Saliha Djenaoui, Pierre Guillon. The generic limit set of cellular automata. 2017. ⟨hal-01861590v3⟩