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arXiv 2005.074512020-05math.DS

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

Hui Rao, Ya-min Yang, Yuan Zhang

英文摘要：

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

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