Elastic curves and Willmore Hopf-Tori

Whitham deformationIncreasing the spectral genusIncreasing the spectral genusLemmaLet X be a polynomial Killing field. Then (λ 2 − a 2 ) X for a ∈ R isa polynomial Killing field, and both induce the same curve.Opening double points:◮ Suppose a ∈ R is a double point on Σ.◮ Then µ(a) = ±1 and writed log µ =(λ2 − a 2 ) B(λ 2 − a 2 ) √ A dλ .◮ Now can pick initial condition for the flow at t = 0 such thatwhen t > 0 the roots ±a move vertically off the real axis.