Multifractal decompositions of Moran fractals
Multifractal decompositions of Moran fractals
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DOI：
10.1016/0001-8708(92)90064-r
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发表时间：
1992-04
影响因子：
1.7
通讯作者：
R. Cawley;And R Daniel Mauldin
中科院分区：
文献类型：
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作者：
R. Cawley;And R Daniel Mauldin
我们提出了具有无限乘积测度的莫兰分形的多重分形分解的严格构造和推广。泛化由分区和中的非负权重系统指定。在权重等于 1 的情况下，恢复了 f(α) 理论的所有常见（平滑）性质。广义谱 f(α,w) 对于权重的一组规范变换是不变的，此外，不再需要是凹的。如果分形是由相似性迭代函数系统生成的康托集，则 α 是测度的逐点维数。我们讨论一些例子的属性。
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 thef(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.