Multifractal spectra and multifractal zeta-functions

Vuksan Mijovic; Lars Ole Ronnow Olsen

doi:10.1007/s00010-016-0451-x

Multifractal spectra and multifractal zeta-functions

Vuksan Mijovic, Lars Ole Ronnow Olsen

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce multifractal zetafunctions providing precise information of a very general class of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic Birkhoff averages of continuous functions. More precisely, we prove that these and more general multifractal spectra equal the abscissae of convergence of the associated zeta-functions.

Original language	English
Pages (from-to)	21-82
Number of pages	62
Journal	Aequationes Mathematicae
Volume	91
Issue number	1
Early online date	31 Dec 2016
DOIs	https://doi.org/10.1007/s00010-016-0451-x
Publication status	Published - Feb 2017

Keywords

Multifractals
Zeta functions
Large deviations
Ergodic theory
Hausdorff dimension

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Mijovic_2016_Multifractal_AM_CC
© The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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Cite this

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KW - Zeta functions

KW - Large deviations

KW - Ergodic theory

KW - Hausdorff dimension

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Multifractal spectra and multifractal zeta-functions

Abstract

Keywords

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