Journal of Statistical Physics, Vol. 76, Nos. 3/4. 1994, p. 929-967.
We introduce an integrable isochronous system and perturb its frdquency by an external~eterministic or purely random — noise. Under the perturbation the action variable evolves in time: the corresponding diffusion coefficient is exactly computed and its dependence on the magnitude of the perturbation is carefully investigated. Different behaviors are found and justified: the quasilinear approximation, the superlinear regime, and the ballistic motion.