Open Access
2015 Homogeneous Multifractal Measures with Disjoint Spectrum and Monohölder Monotone Functions
Zoltán Buczolich, Stéphane Seuret
Real Anal. Exchange 40(2): 277-290 (2015).


We proved in an earlier paper that the support of the multifractal spectrum of a homogeneously multifractal (HM) measure within $[0,1]$ must be an interval. In this paper we construct a homogeneously multifractal measure with spectrum supported by $[0,1] \cup \{ 2\}$. This shows that there can be a different behaviour for exponents exceeding one.

We also provide details of the construction of a strictly monotone increasing monohölder (and hence HM) function which has exact Hölder exponent one at each point. This function was also used in our paper about measures and functions with prescribed homogeneous multifractal spectrum.


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Zoltán Buczolich. Stéphane Seuret. "Homogeneous Multifractal Measures with Disjoint Spectrum and Monohölder Monotone Functions." Real Anal. Exchange 40 (2) 277 - 290, 2015.


Published: 2015
First available in Project Euclid: 4 April 2017

zbMATH: 06848836

Primary: 26A16 , 28A80
Secondary: 28A78

Keywords: Holder exponent , homogeneously multifractal , multifractal spectrum

Rights: Copyright © 2015 Michigan State University Press

Vol.40 • No. 2 • 2015
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