  Nowadays, divertors are used in the main tokamaks to control the magnetic
field and to improve the plasma confinement. In this article, we present
analytical symplectic maps describing Poincar\'e maps of the magnetic field
lines in confined plasmas with a single null poloidal divertor. Initially, we
present a divertor map and the tokamap for a diverted configuration. We also
introduce the Ullmann map for a diverted plasma, whose control parameters are
determined from tokamak experiments. Finally, an explicit, area-preserving and
integrable magnetic field line map for a single-null divertor tokamak is
obtained using a trajectory integration method to represent toroidal
equilibrium magnetic surfaces. In this method, we also give examples of onset
of chaotic field lines at the plasma edge due to resonant perturbations.
