Abstract
We present a rigorous construction and generalization of the multifractal decomposition for Moran fractals with infinite product measure. The generalization is specified by a system of nonnegative weights in the partition sum. All the usual (smooth) properties of the f( α) theory are recovered for the case that the weights are equal to unity. The generalized spectrum, f( α, w), is invariant to a group of gauge transformations of the weights, and, in addition, need no longer be concave. In case the fractal is a Cantor set generated by an iterated function system of similarities, α is the pointwise dimension of the measure. We discuss properties of some examples.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
