Equicontinuity of maps on dendrites

Given a dendrite X and a continuous map f: X → X, we show the following are equivalent: (i) ωf is continuous and Per(f)¯=⋂n∈Nfn(X); (ii) ω(x,f)=Ω(x,f) for each x ∈ X; and (iii) f is equicontinuous. Furthermore, we present some examples illustrating our results.

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Bibliographic Details
Published in:	Chaos, solitons and fractals Vol. 126; pp. 1 - 6
Main Authors:	Camargo, Javier, Rincón, Michael, Uzcátegui, Carlos
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01-09-2019
Subjects:	Secondary: 37B45 Primary: 54H20
Online Access:	Get full text
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Description
Summary:	Given a dendrite X and a continuous map f: X → X, we show the following are equivalent: (i) ωf is continuous and Per(f)¯=⋂n∈Nfn(X); (ii) ω(x,f)=Ω(x,f) for each x ∈ X; and (iii) f is equicontinuous. Furthermore, we present some examples illustrating our results.
ISSN:	0960-0779 1873-2887
DOI:	10.1016/j.chaos.2019.05.033