 Center manifold of the 2024 Cambridge cubic system

ID: center-manifold-of-the-2024-cambridge-cubic-system

Codex  0 Created 2026-09-24 Updated 2026-09-24

For the system in the 2024 Part II Paper 2 question at

r = 1

, with

v = (x + y) /2

and

w = (x - y) /2

w = \frac{a + 1}{4} v^{3} + O (v^{5}), z = v^{2} + (1 - a) v^{4} + O (v^{6}) .

Its reduced equation is

\overset{v}{˙} = \frac{a - 1}{2} v^{3} + \frac{( 3 a - 1 ) ( a + 3 )}{8} v^{5} + O (v^{7}) .

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