Dendrites and chaos

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 $\omega$-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 $\omega$-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.

21 pages, 2 figures

References in corpus (1)

• Two results on entropy, chaos, and independence in symbolic dynamics

Cited by in corpus (2)

• Distributional Chaos and Dendrites
• $\omega$-chaos without infinite LY-scrambled set on Gehman dendrite