  In this paper we consider the Euler-Poisson system (describing a plasma made
of ions with a negligible ion temperature) on the Sobolev spaces $H^s(\R^3)$,
$s > 5/2$. Using a geometric approach we show that for any time $T > 0$ the
corresponding solution map, $(\rho_0,u_0) \mapsto (\rho(T),u(T))$, is nowhere
locally uniformly continuous. On the other hand it turns out that the
trajectories of the ions are analytic curves in $\R^3$.
