English

$\omega$-chaos without infinite LY-scrambled set on Gehman dendrite

Dynamical Systems 2019-06-26 v1

Abstract

We answer the last question left open in [Z.~Ko\v{c}an, \emph{Chaos on one-dimensional compact metric spaces}, Internat. J. Bifur. Chaos Appl. Sci. Engrg. \textbf{22}, article id: 1250259 (2012)] which asks whether there is a relation between an infinite LY-scrambled set and ω\omega-chaos for dendrite maps. We construct a continuous self-map of a dendrite without an infinite LY-scrambled set but containing an uncountable ω\omega-scrambled set.

Keywords

Cite

@article{arxiv.1810.02944,
  title  = {$\omega$-chaos without infinite LY-scrambled set on Gehman dendrite},
  author = {Tomasz Drwięga and Piotr Oprocha},
  journal= {arXiv preprint arXiv:1810.02944},
  year   = {2019}
}