Reference : Pointwise regularity of parameterized affine zipper fractal curves fractal curves
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/34159
Pointwise regularity of parameterized affine zipper fractal curves fractal curves
English
Bárány, Balázs [Budapest University of Technology and Economy > Stochastic department]
Kiss, Gergely mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Kolossváry, István [Alfréd Rényi Institute of Mathematics]
Mar-2018
Nonlinearity
Institute of Physics
31
5
Yes (verified by ORBilu)
International
0951-7715
[en] affine zippers ; pointwise Hölder exponent ; multifractal analysis ; pressure function ; iterated function system ; de Rham curve
[en] 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.
F1R-MTH-PUL-15MRO3
http://hdl.handle.net/10993/34159
10.1088/1361-6544

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