On Limit Sets of Monotone Maps on Dendroids

Let be a dendrite, : → be a monotone map. In the papers by I. Naghmouchi (2011, 2012) it is shown that -limit set ) of any point ∈ has the next properties: In the paper by E. Makhrova, K. Vaniukova (2016 ) it is proved that The aim of this note is to show that the above results – do not hold for mon...

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Bibliographic Details
Published in:Applied mathematics and nonlinear sciences 2020-07, Vol.5 (2), p.311-316
Main Author: Makhrova, E.N.
Format: Article
Language:English
Subjects:
37B20
37C25
54F50
54H20
dendrite
dendroid
limit set
monotone map
non-wandering point
periodic point
ω-limit set
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Summary:Let be a dendrite, : → be a monotone map. In the papers by I. Naghmouchi (2011, 2012) it is shown that -limit set ) of any point ∈ has the next properties: In the paper by E. Makhrova, K. Vaniukova (2016 ) it is proved that The aim of this note is to show that the above results – do not hold for monotone maps on dendroids.
ISSN:2444-8656
2444-8656
DOI:10.2478/amns.2020.2.00056