SELF-SIMILARITY, LP-SPECTRUM AND MULTIFRACTAL FORMALISM
SELF-SIMILARITY, LP-SPECTRUM AND MULTIFRACTAL FORMALISM
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DOI：
10.1007/978-3-0348-7755-8_4
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
K. Lau
中科院分区：
文献类型：
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作者：
K. Lau
这是对围绕 Lp 谱及其与局部维数谱的关系的自相似度量的近期工作的说明性调查。这种关系就是物理学家提出的多重分形形式主义。我们这里要严肃对待形式主义。将详细讨论开集条件和新的较弱分离条件；将介绍几种计算 Lp 谱的技术；并讨论满足二尺度膨胀方程的函数的多重分形结构。
This is an expository survey of recent work on self-similar measures centered around theLp-spectrum and its relationship to the local dimension spectrum. The relationship is the multifractal formalism proposed by physicists. We will treat the formalism rigorously here. The open set condition and a new weaker separation condition will be discussed in detail; several techniques for calculating theLp-spectrum will be introduced; and the multifractal structure of functions satisfying the two-scale dilation equations will also be discussed.