Dynamics in multiplicative processes

We study the dynamics on fractals generated by multiplicative processes. The fractal's elements are the transition rates {wi} in one-dimensional systems. We find a general relation for dynamics dw=1-τ(1), where dw is the exponent characterizing the mean-square displacement, & and τ(q) characterize the scaling of the qth moment of the fractal elements with its size. We show that criticality in dw occurs only when f(α) spectra are discrete.