$\omega$-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 -chaos for dendrite maps. We construct a continuous self-map of a dendrite without an infinite LY-scrambled set but containing an uncountable -scrambled set.
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}
}