Abstract

We characterize dendrites DD such that a continuous selfmap of DD is generically chaotic (in the sense of Lasota) if and only if it is generically ε\varepsilon-chaotic for some ε>0\varepsilon>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 DD belongs to this class if and only if it is completely regular, with all points of finite order (that is, if and only if DD contains neither a copy of the Riemann dendrite nor a copy of the ωω-star).

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