Eugene BELOKOLOS
Institute of Magnetism of NAS of Ukraine,
It is possible to define such a Poisson structure that the functions $z(w)$, $\overline{z}(w^{-1})$ appeared to be a conjugate variables with respect to this structure. Here $z(w)$ is a univalent conformal map of the exterior of the unit disc to the exterior of the domain. Deformations of the functions $z(w)$, $\overline{z}(w^{-1})$ with respect to the moments appeared to be the Hamiltonian equations where the Hamiltonians are partial derivatives of the Schwarz function potential with respect to the moments. These equations  are known as the Lax-Sato equations.