Dimension of slices through a self-similar set with initial cubic pattern (Q2860879)
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scientific article; zbMATH DE number 6225481
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dimension of slices through a self-similar set with initial cubic pattern |
scientific article; zbMATH DE number 6225481 |
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Dimension of slices through a self-similar set with initial cubic pattern (English)
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11 November 2013
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Hausdorff dimension
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self-similar set
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slice
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box dimension
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Marstrand theorem
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As it is well known, the Hausdorff dimension has a crucial importance in fractals theory but, at the same time, it is, with few exceptions, difficult to calculate for fractal sets. Based of the results of Marstrand and Mattila the authors of this paper consider the Marstrand's value of Hausdorff dimension of self-similar sets and establish that, under sufficient assumption, the Hausdorff dimension of slices of a self-similar set in a fixed direction is the dimension of the respective set minus one.
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