Multifractal spectra and multifractal zeta-functions

Vuksan Mijovic, Lars Ole Ronnow Olsen

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)21-82
Number of pages62
JournalAequationes Mathematicae
Volume91
Issue number1
Early online date31 Dec 2016
DOIs
Publication statusPublished - Feb 2017

Keywords

  • Multifractals
  • Zeta functions
  • Large deviations
  • Ergodic theory
  • Hausdorff dimension

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