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Paper

Pointwise regularity of parameterized affine zipper fractal curves

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Published 27 March 2018 • © 2018 IOP Publishing Ltd & London Mathematical Society
, , Citation Balázs Bárány et al 2018 Nonlinearity 31 1705 DOI 10.1088/1361-6544/aaa497

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Author e-mails

balubsheep@gmail.com

kigergo57@gmail.com

istvanko@math.bme.hu

Author affiliations

1 Budapest University of Technology and Economics, Institute of Mathematics, Department of Stochastics, MTA-BME Stochastics Research Group, PO Box 91, 1521 Budapest, Hungary

2 Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

3 Faculty of Science, University of Luxembourg, Luxembourg City, Luxembourg

4 Department of Stochastics, Budapest University of Technology and Economics, Institute of Mathematics, Budapest, Hungary

5 MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

Dates

  1. Received 12 September 2016
  2. Accepted 2 January 2018
  3. Published

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0951-7715/31/5/1705

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.

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10.1088/1361-6544/aaa497