Multifractal Decompositions of Moran Fractals
نویسندگان
چکیده
We present a rigorous construction and generalization of the multifractal decomposition for Moran fractals with intinite product measure. The generalization is specilied by a system of nonnegative weights in the partition sum. All the usual (smooth) properties of thef(a) theory are recovered for the case that the weights are equal to unity. The generalized spectrum, !(a, r~), 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, a is the pointwise dimension of the measure. We discuss properties of some examples.
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