  Vortex dynamics in a thin superfluid ${}^4$He film as well as in a type II
superconductor is described by the classical counterpart of the model advocated
by Peierls, and used for deriving the ground states of the Fractional Quantum
Hall Effect. The model has non-commuting coordinates, and is obtained by
reduction from a particle associated with the ``exotic'' extension of the
planar Galilei group.
