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arXiv 0802.00642008-02-01math.DSmath.PR

V-变量分形：部分自相似分形

V-Variable Fractals: Fractals with Partial Self Similarity

Michael Barnsley, John E. Hutchinson, Örjan Stenflo

备注：: 33 pages, 3 figures

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摘要：

我们建立了一种新的分形性质，它在所有尺度上都具有部分自相似性。对于任何具有相关概率分布和任何正整数V的迭代函数系统的集合，存在相应的V-变量分形集或测度类。这些V-变量分形可以从单个确定性迭代函数系统的吸引子上的点得到。在平均压缩性假设下，得到了解的存在唯一性和逼近结果。我们还得到了迭代函数系的一些基本结果的推广。

英文摘要：

We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a corresponding class of V-variable fractal sets or measures. These V-variable fractals can be obtained from the points on the attractor of a single deterministic iterated function system. Existence, uniqueness and approximation results are established under average contractive assumptions. We also obtain extensions of some basic results concerning iterated function systems.

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