Lipschitz equivalence of a class of self-similar sets with complete overlaps (Q2906163)
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scientific article; zbMATH DE number 6077177
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lipschitz equivalence of a class of self-similar sets with complete overlaps |
scientific article; zbMATH DE number 6077177 |
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Lipschitz equivalence of a class of self-similar sets with complete overlaps (English)
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5 September 2012
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fractals
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self-similar set
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Lipschitz equivalence
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complete overlaps
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Fix \(r \in (0, 1 / 3]\). Let \(\{K_n\}_{n=1}^\infty\) be a class of self-similar sets satisfying NEWLINE\[NEWLINEK_n = (r K_n) \cup (rK_n + r^n (1 - r)) \cup (r K_n + 1-r).NEWLINE\]NEWLINE NEWLINEThen the authors prove that, for any \(n_1, n_2 \geq 1\), \(K_{n_1}\) and \(K_{n_2}\) are Lipschitz equivalent.
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