Pointwise regularity of parameterized affine zipper fractal curves fractal curves

Reference : Pointwise regularity of parameterized affine zipper fractal curves fractal curves


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/34159

Title :	Pointwise regularity of parameterized affine zipper fractal curves fractal curves
Language :	English
Author, co-author :	Bárány, Balázs [Budapest University of Technology and Economy > Stochastic department]
	Kiss, Gergely [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
	Kolossváry, István [Alfréd Rényi Institute of Mathematics]
Publication date :	Mar-2018
Journal title :	Nonlinearity
Publisher :	Institute of Physics
Volume :	31
Issue/season :	5
Peer reviewed :	Yes (verified by ORBi^lu)
Audience :	International
ISSN :	0951-7715
Keywords :	[en] affine zippers ; pointwise Hölder exponent ; multifractal analysis ; pressure function ; iterated function system ; de Rham curve
Abstract :	[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.
Name of the research project :	F1R-MTH-PUL-15MRO3
Permalink :	http://hdl.handle.net/10993/34159
DOI :	10.1088/1361-6544/AAA497

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Open access	Zipper.pdf		Publisher postprint	601.24 kB	View/Open

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