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The paper deals with the existence of nonstationary collision-free periodicsolutions of singular first order Hamiltonian systems of $N$-vortex type in adomain $\Omega\subset\mathbb{C}$. 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 \[ H_\Omega(z_1,\dots,z_N)  = -\sum_{{j,k=1}\over{j\ne k}}^N \frac{1}{2\pi}\log|z_j-z_k| -\sum_{j,k=1}^Ng(z_j,z_k). \] The function $g:\Omega\times\Omega\to\mathbb{R}$ is required tobe of class $C^3$ and symmetric, the regular part of a hydrodynamic Greenfunction being our model. The Hamiltonian is unbounded from above and below,and the associated action integral is not defined on an open subset of thespace 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 presentquite general conditions on the behavior of $g$ near $\Gamma$ which imply thatthere 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 arechoreographies, 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 vortexwith the curvature of $\Gamma$.

Periodic solutions of N-vortex type Hamiltonian systems near the domain boundary