The generic limit set of cellular automata

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

The generic limit set of cellular automata

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

Cantor equicontinuous factors of the Coven cellular automaton of three neighbours

International audienceWe prove a sucient condition for the non-existence of a nontrivial Cantor equicontinuous factor in dynamical systems. We study the Coven cellular automaton of three neighbours to show that it does not have a nontrivial Cantor equicontinuous factor. Through this study, we show that the blocking words in this cellular automaton are all of the same form

The generic limit set of cellular automata

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