Last Updated:2025/12/31
Sentence
The
equivalency
arises
when
we
add
condition
of
invariance
to
Li-Yorke
scrambled
set.
In
this
note
we
show
that
for
a
continuous
graph
map
properties
positive
topological
entropy;
horseshoe;
invariant
Li-Yorke
scrambled
set;
uniform
invariant
distributional
chaotic
scrambled
set
and
distributionaly
chaotic
pair
are
mutually
equivalent..
Quizzes for review
The equivalency arises when we add condition of invariance to Li-Yorke scrambled set. In this note we show that for a continuous graph map properties positive topological entropy; horseshoe; invariant Li-Yorke scrambled set; uniform invariant distributional chaotic scrambled set and distributionaly chaotic pair are mutually equivalent..
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