  It is shown that the dynamics of the growth of a two dimensional surface in a
Laplacian field can be mapped onto Hamiltonian dynamics. The mapping is carried
out in two stages: first the surface is conformally mapped onto the unit
circle, generating a set of singularities. Then the dynamics of these
singularities are transformed to Hamiltonian action-angle variables. An
explicit condition is given for the existence of the transformation. This
formalism is illustrated by solving explicitly for a particular case where the
result is a separable and integrable Hamiltonian.
