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Pointwise regularity of parameterized affine zipper fractal curves
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Bárány, Balazs, Kiss, Gergely and Kolossváry, István (2018) Pointwise regularity of parameterized affine zipper fractal curves. Nonlinearity, 31 (5). pp. 1705-1733. doi:10.1088/1361-6544/aaa497 ISSN 0951-7715.
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Official URL: http://dx.doi.org/10.1088/1361-6544/aaa497
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.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | Nonlinearity | ||||||
Publisher: | Institute of Physics Publishing Ltd. | ||||||
ISSN: | 0951-7715 | ||||||
Official Date: | 27 March 2018 | ||||||
Dates: |
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Volume: | 31 | ||||||
Number: | 5 | ||||||
Page Range: | pp. 1705-1733 | ||||||
DOI: | 10.1088/1361-6544/aaa497 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access |
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