Generic chaos on dendrites

Abstract

AbstractWe characterize dendritesDsuch that a continuous selfmap ofDis generically chaotic (in the sense of Lasota) if and only if it is generically${\varepsilon }$-chaotic for some${\varepsilon }>0$. 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 non-empty interiors under iterates of the map. A dendriteDbelongs to this class if and only if it is completely regular, with all points of finite order (that is, if and only ifDcontains neither a copy of the Riemann dendrite nor a copy of the$\omega $-star).