Multifractal spectra of random self-affine multifractal Sierpiński sponges in \(\mathbb{R}^d\) (Q2909236)
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scientific article; zbMATH DE number 6074008
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multifractal spectra of random self-affine multifractal Sierpiński sponges in \(\mathbb{R}^d\) |
scientific article; zbMATH DE number 6074008 |
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30 August 2012
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multifractals
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self-affine measures
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Sierpinski sponges
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Hausdorff dimension
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local dimension
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Multifractal spectra of random self-affine multifractal Sierpiński sponges in \(\mathbb{R}^d\) (English)
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The authors provide almost sure formulas for the Hausdorff multifractal spectrum of certain classes of random self-affine multifractal Sierpiński sponges in \(\mathbb R^d\). This is done by recalling the definition of classical (non-random) self-affine multifractal Sierpiński sponges in \(\mathbb R^d\) introduced by Bedford [Ph.D. Dissertation, University of Warwick, (1984)] and \textit{C. McMullen} [Nagoya Math. J. 96, 1--9 (1984; Zbl 0539.28003)], and by carefully presenting the definition of random self-affine multifractal Sierpiński sponges.
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