A widespread technique in the study of continuous systems is their association with discrete systems. This happens, for example, when numerical methods are used to integrate the di erential equations describing the continuous system or when the Poincare map is considered for discretization. In this procedure, the analogy of the dynamic properties of the two systems is crucial. For classical numerical methods, this means to use a small enough integration step but the problem is more complicated for Poincare maps. In this paper we point out some problems that occur in the study of Poincare models associated with Hamiltonian systems with 3/2 degrees fo freedom. These models are obtained using a symmetric mapping technique, which is a classical method in the study of Hamiltonian systems. It is observed that some orbits are chaotic or not, depending on the mapping step. A local criterion for determining the optimal mapping step for the preservation of the dynamical characteristics (regular or chaotic) of an orbit is proposed. A global criterion is also derived. These criteria are applied for the study of a Hamiltonian system modeling the magnetic eld con guration in tokamak.