Are there known examples of dynamical systems, iterated functions systems, random processes, ... where the multifractal spectrum f(alpha) is linear in alpha (e.g. f(alpha)=alpha), or are there mathematical obstructions to this ?
Given the curve f(alpha) vs. alpha, the line g(alpha)=alpha is tangent to the curve at a value corresponding to D_1, the average fractal dimension of the measure. This *means* that around this value, f(alpha) is linear in alpha to first order.