Tomasz Drwięga | Searcharxiv

arXiv2018

$ω$-chaos without infinite LY-scrambled set on Gehman dendrite

We answer the last question left open in [Z.~Kočan, \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 $ω$-chaos for dendrite maps. We construct a continuous self-map of a dendrite without an infinite LY-scrambled set but containing an uncountable $ω$-scrambled set.

math.DS↗

arXiv2018

Dendrites and chaos

We answer the two questions left open in [Z.~Kočan, Internat. J. Bifur. Chaos Appl. Sci. Engrg. \textbf{22}, article id: 125025 (2012)] i.e. whether there is a relation between $ω$-chaos and distributional chaos and whether there is a relation between an infinite LY-scrambled set and distributional chaos for dendrite maps. We construct a continuous self-map of dendrite without any \textit{DC3} pairs but containing an uncountable $ω$-scrambled set. To answer for the second question we construct dendrite $\mathcal{D}$ and continuous dendrite map without an infinite LY-scrambled set but with \textit{DC1} pairs.

math.DS↗