  The paper deals with the existence of nonstationary collision-free periodic
solutions of singular first order Hamiltonian systems of $N$-vortex type in a
domain $\Omega\subset\mathbb{C}$. These are solutions
$z(t)=(z_1(t),\dots,z_N(t))$ of \[ \dot{z}_j(t)=-i\nabla_{z_j}
H_\Omega\big(z(t)\big),\quad j=1,\dots,N, \tag{HS} \] where the Hamiltonian
$H_\Omega$ has the form \[ H_\Omega(z_1,\dots,z_N)
  = -\sum_{{j,k=1}\over{j\ne k}}^N \frac{1}{2\pi}\log|z_j-z_k| -\sum_{j,k=1}^N
g(z_j,z_k). \] The function $g:\Omega\times\Omega\to\mathbb{R}$ is required to
be of class $C^3$ and symmetric, the regular part of a hydrodynamic Green
function being our model. The Hamiltonian is unbounded from above and below,
and the associated action integral is not defined on an open subset of the
space of periodic $H^{1/2}$ functions.
  Given a closed connected component $\Gamma\subset\partial\Omega$ of class
$C^3$ we are interested in periodic solutions of (HS) near $\Gamma$. We present
quite general conditions on the behavior of $g$ near $\Gamma$ which imply that
there exists a family of periodic solutions $z^{(r)}(t)$, $0<r<\overline{r}$,
with arbitrarily small minimal period $T_r\to0$ as $r\to0$, and such that the
"point vortices" $z_j^{(r)}(t)$ approach $\Gamma$ as $r\to0$. The solutions are
choreographies, i.e.\ $z_j^{(r)}(t)$ moves on the same trajectory as
$z_1^{(r)}(t)$ with a phase shift. We can also relate the speed of each vortex
with the curvature of $\Gamma$.
