  We study how the orbits of the singularities of the inverse of a meromorphic
function prescribe the dynamics on its Julia set, at least up to a set of
(Lebesgue) measure zero. We concentrate on a family of entire transcendental
functions with only finitely many singularities of the inverse, counting
multiplicity, all of which either escape exponentially fast or are
pre-periodic. For these functions we are able to decide, whether the function
is recurrent of not. In the case that the Julia set is not the entire plane we
also obtain estimates for the measure of the Julia set.
