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The chaotic diffusion for a family of Hamiltonian mappings whose anglesdiverge in the limit of vanishingly action is investigated by using thesolution of the diffusion equation. The system is described by atwo-dimensional mapping for the variables action, $I$, and angle, $\theta$ andcontrolled by two control parameters: (i) $\epsilon$, controlling thenonlinearity of the system, particularly a transition from integrable for$\epsilon=0$ to non-integrable for $\epsilon\ne0$ and; (ii) $\gamma$ denotingthe 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 finitediffusion in the action characterized by the solution of the diffusionequation. The analytical solution is then compared to the numerical simulationsshowing a remarkable agreement between the two procedures.

An investigation of chaotic diffusion in a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action