Pointwise regularity of parameterized affine zipper fractal curves

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 characteri...

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Bibliographic Details
Published in:Nonlinearity 2018-03, Vol.31 (5), p.1705-1733
Main Authors: Bárány, Balázs, Kiss, Gergely, Kolossváry, István
Format: Article
Language:English
Subjects:
affine curves
de Rham function
iterated function scheme
multifractal analysis
pointwise Hölder exponents
pressure function
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Summary: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.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aaa497