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Open AccessArticle

Some Chaos Notions on Dendrites

Center of Modelling and Data Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Malaysia
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Symmetry 2019, 11(10), 1309; https://doi.org/10.3390/sym11101309
Received: 15 September 2019 / Revised: 5 October 2019 / Accepted: 8 October 2019 / Published: 17 October 2019
(This article belongs to the Special Issue Symmetry and Dynamical Systems)
Transitivity is a key element in a chaotic dynamical system. In this paper, we present some relations between transitivity, stronger and alternative notions of it on compact and dendrite spaces. The relation between Auslander and Yorke chaos and Devaney chaos on dendrites is also discussed. Moreover, we prove that Devaney chaos implies strong dense periodicity on dendrites while the converse is not true. View Full-Text
Keywords: dendrite; transitive; locally everywhere onto; mixing; weakly mixing; blending; accessible endpoint; Devaney chaos; Auslander and Yorke chaos; strong dense periodicity dendrite; transitive; locally everywhere onto; mixing; weakly mixing; blending; accessible endpoint; Devaney chaos; Auslander and Yorke chaos; strong dense periodicity
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MDPI and ACS Style

Fadel, A.; Dzul-Kifli, S.C. Some Chaos Notions on Dendrites. Symmetry 2019, 11, 1309.

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