Dynamics in multiplicative processes

We study the dynamics on fractals generated by multiplicative processes. The fractal’s elements are the transition rates {$w_i$} in one-dimensional systems. We find a general relation for dynamics $d_w$=1-τ(1), where $d_w$ 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 $d_w$ occurs only when f(α) spectra are discrete.