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Center manifold of the 2024 Cambridge cubic system
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Center manifold
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For the system in the 2024 Part II Paper 2 question at
r
=
1
, with
v
=
(
x
+
y
)
/2
and
w
=
(
x
−
y
)
/2
, the center manifold is
w
=
4
a
+
1
v
3
+
O
(
v
5
)
,
z
=
v
2
+
(
1
−
a
)
v
4
+
O
(
v
6
)
.
(6)
Its reduced equation is
v
˙
=
2
a
−
1
v
3
+
8
(
3
a
−
1
)
(
a
+
3
)
v
5
+
O
(
v
7
)
.
(7)
Ancestors
(5)
Center manifold
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