Diffusion in models of modulated area-preserving maps

We investigate the diffusion in the action variable when the frequency of an integrable isochronous map is modulated. Purely stochastic, hyperbolic, or periodic deterministic modulations are considered. The diffusion coefficient in the invariant for the unperturbed map is exactly determined and shown to be nonzero, except in the last case, when the modulation is smooth and nonzero, due to the presence of topological barriers