Results 11 to 20 of about 90 (88)

A Systematic Study of Multifractal Measures and Dimensions for Image Measures on Moran Sets

Abstract and Applied Analysis
MSC2020 Classification: 28A20, 28A75, 28A78, 28A80 ...
Lixin Guo, Haythem Zyoudi
doaj   +2 more sources

How long is the chaos game?

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

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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Structure of equilibrium states on self‐affine sets and strict monotonicity of affinity dimension

Proceedings of the London Mathematical Society, Volume 116, Issue 4, Page 929-956, April 2018., 2018
Abstract A fundamental problem in the dimension theory of self‐affine sets is the construction of high‐dimensional measures which yield sharp lower bounds for the Hausdorff dimension of the set. A natural strategy for the construction of such high‐dimensional measures is to investigate measures of maximal Lyapunov dimension; these measures can be ...
Antti Käenmäki, Ian D. Morris
wiley   +1 more source

Fractal and fractional dynamics for a 3D autonomous and two-wing smooth chaotic system

Alexandria Engineering Journal, 2020
Some existing chaotic systems cannot display dynamics with attractors showing a fractal representation. This is due, not only to the nature of the phenomenon under description, but also to the type of derivative operator used to express the whole model ...
Emile F. Doungmo Goufo
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Function spaces on the Koch curve

Journal of Function Spaces, Volume 8, Issue 3, Page 287-299, 2010., 2010
We consider two types of Besov spaces on the Koch curve, defined by traces and with the help of the snowflaked transform. We compare these spaces and give their characterization in terms of Daubechies wavelets.
Maryia Kabanava, Hans Triebel
wiley   +1 more source

Hölder Parameterization of Iterated Function Systems and a Self-Affine Phenomenon

Analysis and Geometry in Metric Spaces, 2021
We investigate the Hölder geometry of curves generated by iterated function systems (IFS) in a complete metric space. A theorem of Hata from 1985 asserts that every connected attractor of an IFS is locally connected and path-connected.
Badger Matthew, Vellis Vyron
doaj   +1 more source