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Let X be a dendrite, f : X → X be a monotone map. In the papers by I. Naghmouchi (2011, 2012) it is shown that ω-limit set ω(x, f ) of any point x ∈ X has the next properties:
\omega (x,f) \subseteq \overline {Per(f)}
, where Per( f ) is the set of periodic points of f ;
ω(x, f ) is either a periodic orbit or a minimal Cantor set.
In the paper by E. Makhrova, K. Vaniukova (2016 ) it is proved that
\Omega (f) = \overline {Per(f)}
, where Ω( f ) is the set of non-wandering points of f.
The aim of this note is to show that the above results (1) – (3) do not hold for monotone maps on dendroids.