ω-chaos without infinite LY-scrambled set on Gehman dendrite
Abstract
We answer the last question left open in [Z.~Kocan, Chaos on one-dimensional compact metric spaces, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 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.
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