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

Recurrence of entire transcendental functions with simple post-singular sets