Pointwise regularity of parameterized affine zipper fractal curves

Balázs Bárány, Gergely Kiss, István Kolossváry

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We study the pointwise regularity of zipper fractal curves generated by affine mappings. Under the assumption of dominated splitting of index-1, we calculate the Hausdorff dimension of the level sets of the pointwise Hölder exponent for a subinterval of the spectrum. We give an equivalent characterization for the existence of regular pointwise Hölder exponent for Lebesgue almost every point. In this case, we extend the multifractal analysis to the full spectrum. In particular, we apply our results for de Rham's curve.
Original languageEnglish
Pages (from-to)1705-1733
Number of pages29
JournalNonlinearity
Volume31
Issue number5
Early online date27 Mar 2018
DOIs
Publication statusPublished - May 2018

Keywords

  • Affine curves
  • Pointwise Hölder exponents
  • Multifractal analysis
  • Pressure function
  • Iterated function scheme
  • de Rahm function

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