Multifractal formalism for generalised local dimension spectra of Gibbs measures on the real line

• Jaerisch, Johannes

• Sumi, Hiroki

Abstract

We extend the multifractal formalism for the local dimension spectrum of a Gibbs measure μ supported on the attractor Λ of a conformal iterated functions system on the real line. Namely, for α∈ℝ, we establish the multifractal formalism for the Hausdorff dimension of the set of x∈Λ for which the μ-measure of a ball of radius rn centred at x obeys a power law rn^α, for a sequence rn→0. This allows us to investigate the Hölder regularity of various fractal functions, such as distribution functions and conjugacy maps associated with conformal iterated function systems.

Journal

• Journal of Mathematical Analysis and Applications

  Journal of Mathematical Analysis and Applications 491 (2), 124246-, 2020-11-15

  Elsevier

Keywords

• Multifractal formalism
• Conformal iterated function systems
• Fractal functions
• Local dimension spectrum

Details

• CRID: 1050571563520750208
• NII Article ID: 120006948924
• DOI: 10.1016/j.jmaa.2020.124246
• HANDLE: 2237/00033226
• ISSN: 0022247X
• Web Site: https://nagoya.repo.nii.ac.jp/records/31044
• Web Site: https://api.elsevier.com/content/article/PII:S0022247X2030408X?httpAccept=text/xml
• Web Site: https://api.elsevier.com/content/article/PII:S0022247X2030408X?httpAccept=text/plain
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN