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Miklós Schweitzer
2018 Miklós Schweitzer
8
8
Part of
2018 Miklós Schweitzer
Problems
(1)
Does there exist a function
Source: Miklós Schweitzer 2018 P8
11/10/2018
Does there exist a piecewise linear, continuous, surjective mapping
f
:
[
0
,
1
]
→
[
0
,
1
]
f: [0,1]\to [0,1]
f
:
[
0
,
1
]
→
[
0
,
1
]
such that
f
(
0
)
=
f
(
1
)
=
0
f(0)=f(1)=0
f
(
0
)
=
f
(
1
)
=
0
, and for all positive integer
n
n
n
,
2.000
1
(
n
−
10
)
<
P
n
(
f
)
<
2.999
9
(
n
+
10
)
2.0001^{(n-10)} <P_n(f)<2.9999^{(n+10)}
2.000
1
(
n
−
10
)
<
P
n
(
f
)
<
2.999
9
(
n
+
10
)
holds, where
P
n
(
f
)
P_n(f)
P
n
(
f
)
is the number of points
x
x
x
such that
f
(
…
f
⏟
n
(
x
)
…
)
=
x
\underbrace{f(\dotsc f}_n(x)\dotsc )=x
n
f
(
…
f
(
x
)
…
)
=
x
?
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