English

Generic chaos on dendrites

Dynamical Systems 2021-02-02 v1

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 ω\omega-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

R2 v1 2026-06-23T22:42:02.607Z