  The chaotic diffusion for a family of Hamiltonian mappings whose angles
diverge in the limit of vanishingly action is investigated by using the
solution of the diffusion equation. The system is described by a
two-dimensional mapping for the variables action, $I$, and angle, $\theta$ and
controlled by two control parameters: (i) $\epsilon$, controlling the
nonlinearity of the system, particularly a transition from integrable for
$\epsilon=0$ to non-integrable for $\epsilon\ne0$ and; (ii) $\gamma$ denoting
the power of the action in the equation defining the angle. For $\epsilon\ne0$
the phase space is mixed and chaos is present in the system leading to a finite
diffusion in the action characterized by the solution of the diffusion
equation. The analytical solution is then compared to the numerical simulations
showing a remarkable agreement between the two procedures.
