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Joined 2026-09-21 Message
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 Incoming links: Equivariant dynamical system

Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 54 / 1 / a / Solution 2026-10-03
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Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 60 / 1 / ii / Solution 2026-10-03
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Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 60 / 1 / i / Solution 2026-10-03
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Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 85 / 3 / a / Solution 2026-10-03
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Wavevector selection rule for equivariant monomials 2026-10-14
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An equivariant dynamical system can contain the monomial ∏j​Ajpj​​Ajqj​​ in its ℓth amplitude equation only if its total wavevector equals the output wavevector. Its degree is ∑j​(pj​+qj​). Thus an integer vector d=p−q contributes at degree N exactly when the wavevector equation holds, ∥d∥1​≤N, and N−∥d∥1​ is even. The extra even degree is supplied by factors ∣Aj​∣2. This finite integer test distinguishes regular saturation terms from phase-sensitive resonance terms.
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Total articles: 5
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