Affiliation:
1. Lobachevsky State University of Nizhny Novgorod , Russia
Abstract
Abstract
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:
(1)
ω
(
x
,
f
)
⊆
Per
(
f
)
¯
\omega (x,f) \subseteq \overline {Per(f)}
, where Per( f ) is the set of periodic points of f ;
(2)
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
(3)
Ω
(
f
)
=
Per
(
f
)
¯
\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.
Subject
Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science
Cited by
1 articles.
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1. On Limit Sets of Monotone Maps on Regular Curves;Qualitative Theory of Dynamical Systems;2021-09-28