Invariance of multifractal spectrum of uniform self-affine measures and its applications

Hui Rao; Ya-min Yang; Yuan Zhang

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arXiv · 2005.07451

Invariance of multifractal spectrum of uniform self-affine measures and its applications

Hui Rao·Ya-min Yang·Yuan Zhang

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Abstract

We study the bi-Lipschitz classification of Bedford-McMullen carpets which are totally disconnected. Let $E$ be a such carpet and let $\mu_E$ be the uniform Bernoulli measure on $E$. We show that the multifractal spectrum and the doubling property of $\mu_E$ are both invariant under a bi-Lipschitz map. Moreover, we show that if $\mu_E$ and $\mu_F$ are doubling, then a bi-Lipschitz map between $E$ and $F$ enjoys a certain measure preserving property.

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Hui Rao, Ya-min Yang, Yuan Zhang. 2020-05-15. Invariance of multifractal spectrum of uniform self-affine measures and its applications. https://arxiv.org/abs/2005.07451

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