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CIIM
2018 CIIM
Problem 5
Problem 5
Part of
2018 CIIM
Problems
(1)
CIIM 2018 Problem 5
Source:
3/10/2019
Consider the transformation
T
(
x
,
y
,
z
)
=
(
sin
y
+
sin
z
−
sin
x
,
sin
z
+
sin
x
−
sin
y
,
sin
x
+
sin
y
−
sin
z
)
.
T(x,y,z) = (\sin y + \sin z - \sin x,\sin z + \sin x - \sin y,\sin x +\sin y -\sin z).
T
(
x
,
y
,
z
)
=
(
sin
y
+
sin
z
−
sin
x
,
sin
z
+
sin
x
−
sin
y
,
sin
x
+
sin
y
−
sin
z
)
.
Determine all the points
(
x
,
y
,
z
)
∈
[
0
,
1
]
3
(x,y,z) \in [0,1]^3
(
x
,
y
,
z
)
∈
[
0
,
1
]
3
such that
T
n
(
x
,
y
,
z
)
∈
[
0
,
1
]
3
,
T^n(x,y,z) \in [0,1]^3,
T
n
(
x
,
y
,
z
)
∈
[
0
,
1
]
3
,
for every
n
≥
1
n \geq 1
n
≥
1
.
CIIM2018
undergraduate