  We study the existence of (relative) simple choreographies for a class of
Hamiltonian systems describing the interaction of particles in the plane
motivated mainly by the n-vortex type problem. In particular, by constructing
choreographic pseudo-holomorphic spheres, we prove that there exist infinitely
many non-trivial relative choreographies for the identical n-vortex problem
arising from both the Euler equation and the Gross-Pitaevskii equation.
