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arXiv · 1811.04841

Equicontinuity of maps on dendrites

Javier Camargo·Michael Rincón·Carlos Uzcátegui
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Abstract

Given a dendrite $X$ and a continuous map $f\colon X\to X$, we show the following are equivalent: (i) $\omega_f$ is continuous and $\overline{\mathrm{Per}(f)}=\bigcap_{n\in\mathbb{N}}f^n(X)$; (ii) $\omega(x,f)=\Omega(x,f)$ for each $x\in X$; and (iii) $f$ is equicontinuous. Furthermore, we present some examples illustrating our results.

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Javier Camargo, Michael Rincón, Carlos Uzcátegui. 2018-11-12. Equicontinuity of maps on dendrites. https://doi.org/10.1016/j.chaos.2019.05.033

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