Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages
Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages
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DOI：
10.1016/j.matpur.2003.09.007
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发表时间：
2003-12
期刊：
影响因子：
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通讯作者：
L. Olsen
中科院分区：
文献类型：
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作者：
L. Olsen
我们引入并发展了一个统一的多重分形框架。本文开发的框架是基于经验测度变形的概念。这种方法导致了已知结果的显著扩展。然而，我们的方法不仅导致了已知结果的扩展，而且通过考虑非线性变形，为研究一些新的非线性局部特征提供了基础。我们还对所谓的散点的分形结构进行了详细的研究。我们定义了多重分形谱，它提供了关于任意（可能是非线性）变形的单个散点分布的极其精确的定量信息，从而扩展和统一了关于散点行为的许多不同的定性结果。用于证明主要结果的技术取自大偏差理论，与以往文献中的技术完全不同。
We introduce and develope a unifying multifractal framework. The framework developed in this paper is based on the notion of deformations of empirical measures. This approach leads to significant extensions of already know results. However, our approach not only leads to extensions of already know results, but also, by considering non-linear deformations, provides the basis for the study of several new and non-linear local characteristic. We also initiate a detailed study of the fractal structure of so-called divergence points. We define multifractal spectra that provides extremely precise quantitative information about the distribution of individual divergence points of arbitrary (possibly non-linear) deformations, thereby extending and unifying many diverse qualitative results on the behaviour of divergence points. The techniques used in proving the main results are taken from large deviation theory and are completely different from previous techniques in the literature.