Stable set of self map

Eddy Godelle (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

The attracting set and the inverse limit set are important objects associated to a self-map on a set. We call \emph{stable set} of the self-map the projection of the inverse limit set. It is included in the attracting set, but is not equal in the general case. Here we determine whether or not the equality holds in several particular cases, among which are the case of a dense range continuous function on an Hilbert space, and the case of a substitution over left infinite words.

Mots clés: inverse limit of self map; attracting set

Domaines: Théorie des groupes [math.GR]; Algèbres d'opérateurs [math.OA]; Systèmes dynamiques [math.DS]

Eddy Godelle. Stable set of self map. 2009. ⟨hal-00418778⟩