The interaction regions of colliders invariably include strong solenoid fields. Where quadrupoles and dipoles are embedded in the solenoid, the beam dynamics in the combined fields can be complicated to model using the traditional approach of interleaving slices of the different fields. The complexity increases if the design trajectory is offset from the magnetic axis; this is the case, for example, in PEP-II. In this paper, we present maps for combined solenoid, dipole and quadrupole fields that provide a much simpler alternative to the traditional approach, and show that the deviation of the design trajectory from the magnetic axis can be handle in a straightforward manner. We illustrate the techniques presented by reference to the PEP-II interaction region
