Results 11 to 20 of about 127 (112)
A Systematic Study of Multifractal Measures and Dimensions for Image Measures on Moran Sets
Abstract and Applied AnalysisMSC2020 Classification: 28A20, 28A75, 28A78, 28A80 ...
Lixin Guo, Haythem Zyoudi
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Tangent measures of typical measures
, 2015 We prove that for a typical Radon measure μ in ℝd, every non-zero Radon measure is a tangent measure of μ at μ almost every point. This was already shown by T. O'Neil in his Ph.D. thesis from 1994, but we provide a different self-contained proof for this
Sahlsten, Tuomas
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Bulletin of the London Mathematical Society, Volume 53, Issue 6, Page 1749-1765, December 2021., 2021 Abstract In the 1988 textbook Fractals Everywhere, Barnsley introduced an algorithm for generating fractals through a random procedure which he called the chaos game. Using ideas from the classical theory of covering times of Markov chains, we prove an asymptotic formula for the expected time taken by this procedure to generate a δ‐dense subset of a ...
Ian D. Morris, Natalia Jurga
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Graph‐like spaces approximated by discrete graphs and applications
Mathematische Nachrichten, Volume 294, Issue 11, Page 2237-2278, November 2021., 2021 Abstract We define a distance between energy forms on a graph‐like metric measure space and on a suitable discrete weighted graph using the concept of quasi‐unitary equivalence. We apply this result to metric graphs, graph‐like manifolds (e.g. a small neighbourhood of an embedded metric graph) or pcf self‐similar fractals as metric measure spaces with ...
Olaf Post, Jan Simmer
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Dimension of ergodic measures projected onto self‐similar sets with overlaps
Proceedings of the London Mathematical Society, Volume 122, Issue 2, Page 191-206, February 2021., 2021 Abstract For self‐similar sets on R satisfying the exponential separation condition we show that the dimension of natural projections of shift invariant ergodic measures is equal to min{1,h−χ}, where h and χ are the entropy and Lyapunov exponent, respectively. The proof relies on Shmerkin's recent result on the Lq dimension of self‐similar measures. We
Thomas Jordan, Ariel Rapaport
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Graph-directed random fractal interpolation function
, 2021 Barnsley introduced in [1] the notion of fractal interpolation function (FIF). He said that a fractal function is a (FIF) if it possess some interpolation properties.
SOÓS, Anna, SOMOGYI, Ildikó
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On harmonic functions on trees [PDF]
, 2001 46 pages, no figures.-- MSC2000 codes: 28A80, 31B05, 31B25.MR#: MR1837265 (2002h:31011)Zbl#: Zbl 1008.31006We study the asymptotic behaviour of harmonic and p-harmonic functions ...
Pestana, Domingo +3 more
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Dimensions of equilibrium measures on a class of planar self-affine sets [PDF]
, 2018 We study equilibrium measures (K¨aenm¨aki measures) supported on self-affine sets generated by a finite collection of diagonal and anti-diagonal matrices acting on the plane and satisfying the strong separation property.
Fraser, Jonathan M +5 more
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Fractional Perimeters from a Fractal Perspective
Advanced Nonlinear Studies, 2019 The purpose of this paper consists in a better understanding of the fractional nature of the nonlocal perimeters introduced in [L. Caffarelli, J.-M. Roquejoffre and O. Savin, Nonlocal minimal surfaces, Comm. Pure Appl. Math.
Lombardini Luca
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Isoperimetric and Poincaré Inequalities on Non-Self-Similar Sierpiński Sponges: the Borderline Case
Analysis and Geometry in Metric Spaces, 2022 In this paper we construct a large family of examples of subsets of Euclidean space that support a 1-Poincaré inequality yet have empty interior. These examples are formed from an iterative process that involves removing well-behaved domains, or more ...
Eriksson-Bique Sylvester, Gong Jasun
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