Generic chaos on dendrites
Dynamical Systems
2021-02-02 v1
Abstract
We characterize dendrites such that a continuous selfmap of is generically chaotic (in the sense of Lasota) if and only if it is generically -chaotic for some . 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 belongs to this class if and only if it is completely regular, with all points of finite order (that is, if and only if contains neither a copy of the Riemann dendrite nor a copy of the -star).
Cite
@article{arxiv.2102.00486,
title = {Generic chaos on dendrites},
author = {Ľubomír Snoha and Vladimír Špitalský and Michal Takács},
journal= {arXiv preprint arXiv:2102.00486},
year = {2021}
}
Comments
accepted for publication in Ergodic Theory Dynam. Systems