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

2020/05/15 by Rao, Hui, Yang, Ya-min, Zhang, Yuan
#26A16 #28A80 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.07451

Abstract

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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