  We use a shadowing-type lemma in order to analyze the singular, semilinear
elliptic equation describing static self-dual abelian Higgs vortices. Such an
approach allows us to construct new solutions having an \textit{infinite}
number of arbitrarily prescribed vortex points. Furthermore, we obtain the
precise asymptotic profile of the solutions in the form of an approximate
superposition rule, up to an error which is exponentially small.
