@article {2015,
title = {Dispersive deformations of the Hamiltonian structure of Euler{\textquoteright}s equations},
year = {2015},
abstract = {Euler{\textquoteright}s equations for a two-dimensional system can be written in Hamiltonian form, where the Poisson bracket is the Lie-Poisson bracket associated to the Lie algebra of divergence free vector fields. We show how to derive the Poisson brackets of 2d hydrodynamics of ideal fluids as a reduction from the one associated to the full algebra of vector fields. Motivated by some recent results about the deformations of Lie-Poisson brackets of vector fields, we study the dispersive deformations of the Poisson brackets of Euler{\textquoteright}s equation and show that, up to the second order, they are trivial.},
author = {Matteo Casati}
}