Recently there has been renewed interest in the influence of fringe fields on particle dynamics, due to studies that revealed their importance in some cases, as, for example, the proposed Neutrino Factory and muon colliders. In this paper, we present a systematic study of generic fringe field effects. Using as an example a lattice of the proposed Neutrino Factory, we show that fringe fields influence the dynamics of particles at all orders, starting with the linear motion. It is found that the widely used sharp cutoff approximation leads to divergences regardless of the specific fall-off shape of the fields. The results suggest that a careful consideration of fringe field effects in the design stage of small machines for large emittances is always recommended.
