Based on the perturbation theory with multiple scales, we have developed a new technique to study the evolution of particle distribution as a function of oscillation amplitudes in hadron storage rings. With a renormalization scheme for the zeroth‐order term, a uniformly valid perturbations such as the beam‐beam interaction at colliding points, this renormalization scheme results in a functional mapping for the particle distribution, and the diffusion processes of particles in the beam can be studied numerically without resorting to the tracking of individual particles. A case involving a single nonliner kick in the ring is presented to illustrate the method in detail.