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arXiv · 1706.01088

Dendrites and chaos

Tomasz Drwięga
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Abstract

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.

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Tomasz Drwięga. 2018-07-26. Dendrites and chaos. https://doi.org/10.1142/s0218127418501584

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