Poloidal divertors are, more than ever before, a crucial topic for the advancement of magnetic fusion technology. Due to the often non linear and stochastic nature of the plasma edge phenomena, canonical mapping has provided a powerful method at modelling their characteristics, albeit many authors rely on heuristically adapted schemes. Thus, it is reported here a specific and physically consistent map model of the tokamak single null magnetic configuration, assuming plasma-field equilibrium, based on the construction of a fundamental Hamiltonian form. Then, the magnetohydrodynamically non ideal perturbations are introduced through the Rayleigh function of the system. As an illustration, the resulting compact canonical map is applied to the analysis of some of the most relevant features of the edge magnetic topology.