Rigorously diffusive deterministic map

The statistical properties of periodic impulse maps may be obtained from the characteristic functions. Series representations for the characteristic functions, the force correlations, and the momentum diffusion coefficient are presented. These results are applied to the sawtooth map for integer values of the perturbation parameter ε, in which case the series may be summed explicitly. It is found that the diffusion coefficient has the quasilinear value for |ε+2|≥2, it vanishes for ε=-2 and -1, and it is infinite for ε=-3.