Generic chaos on dendrites

Abstract

We characterize dendrites D such that a continuous selfmap of D is generically chaotic (in the sense of Lasota) if and only if it is generically ε-chaotic for some ε > 0. In other words, we characterize dendrites on which generic chaos of a continuous map can be described in terms of the behaviour of subdendrites with nonempty interiors under iterates of the map. A dendrite D belongs to this class if and only if it is completely regular, with all points of finite order (that is, if and only if D contains neither a copy of the Riemann dendrite nor a copy of the ω-star).