Densities of Self-Similar Measures on the Line
Densities of Self-Similar Measures on the Line
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DOI：
10.1080/10586458.1995.10504313
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
R. Strichartz;A. Taylor;T. Zhang
中科院分区：
文献类型：
--
作者：
R. Strichartz;A. Taylor;T. Zhang
We describe algorithms to compute self-similar measures associated to iterated function systems (i.f.s.) on an interval, and more general self-replicating measures that include Hausdorff measure on the attractor of a nonlinear i.f.s. We discuss a variety of error measurements for these algorithms. We then use the algorithms to study density properties of these measures experimentally. By density we mean the behavior of the ratio μ(B r (x)/(2r)α as r → 0, were α is an appropriate dimension. It is well-known that a limit usually does not exist. We have found an intriguing structure associated to these ratios that we call density diagrams. We also use density computations to approximate the exact Hausdorff measure of the attractor of an i.f.s,
