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Center manifold of the 2024 Cambridge cubic system
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Physics
Branch of physics
Dynamical systems
Center manifold
Created
2026-09-24
Updated
2026-09-24
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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
)
.
(1)
Its reduced
equation
is
v
˙
=
2
a
−
1
v
3
+
8
(
3
a
−
1
)
(
a
+
3
)
v
5
+
O
(
v
7
)
.
(2)
Ancestors
(5)
Center manifold
Dynamical systems
Branch of physics
Physics
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Past exam of the mathematics course of the University of Cambridge
/
2024
/
ii
/
Paper 2
/
33A
/
b
/
iii
/
Solution
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