Resumen de Integrability of invariant metrics on the diffeomorphism group of the circle

Adrian Constantin, B. Kolev

• Each Hk Sobolev inner product (k ? 0) defines a Hamiltonian vector field Xk on the regular dual of the Lie algebra of the diffeomorphism group of the circle. We show that only X0 and X1 are bi-Hamiltonian relative to a modified Lie-Poisson structure.