  For tokamaks with uniform magnetic shear, Martin and Taylor have proposed a
symplectic map has been used to describe the magnetic field lines at the plasma
edge perturbed by an ergodic magnetic limiter. We propose an analytical
magnetic field line map, based on the Martin-Taylor map, for a tokamak with
arbitrary safety factor profile. With the inclusion of a non-monotonic profile,
we obtain a nontwist map which presents the characteristic properties of
degenerate systems, as the twin islands scenario, the shearless curve and
separatrix reconnection. We estimate the width of the islands and describe
their changes of shape for large values of the limiter current. From our
numerical simulations about the shearless curve, we show that its position and
aspect depend on the control parameters.
