Results 1 to 10 of about 1,536 (100)
A class of continua that are not attractors of any IFS [PDF]
Open Mathematics, 2012 This paper presents a sufficient condition for a continuum in $R^n$ to be embeddable in $R^n$ in such a way that its image is not an attractor of any iterated function system.
Kulczycki Marcin, Nowak Magdalena
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Almost uniform domains and Poincaré inequalities
Transactions of the London Mathematical Society, 2021 Here we show existence of many subsets of Euclidean spaces that, despite having empty interior, still support Poincaré inequalities with respect to the restricted Lebesgue measure.
Sylvester Eriksson‐Bique, Jasun Gong
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Persistence landscapes of affine fractals
Demonstratio Mathematica, 2022 We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility condition, we ...
Catanzaro Michael J. +2 more
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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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Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]
Demonstratio Mathematica, 2021 Cantor sets are constructed from iteratively removing sections of intervals. This process yields a cumulative distribution function (CDF), constructed from the invariant Borel probability measure associated with their iterated function systems.
Byars Allison +5 more
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Representations of real numbers induced by probability distributions on $\mathbb{N}$
, 2021 We observe that a probability distribution supported by $\mathbb{N}$, induces a representation of real numbers in [0, 1) with digits in $\mathbb{N}$.
Neunhäuserer, Jörg
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Cyclic weak ϕ iterated function system
Topological Algebra and its Applications, 2022 In this article, we are considering the cyclic weak ϕ-contraction and prove that the result is also true in Hausdorff metric space. We are constructing a cyclic weak ϕ iterated function system (IFS), which gives the self-referential set or attractor ...
Ullah Kifayat, Katiyar S. K.
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On the structure of self-affine Jordan arcs in ℝ2
Demonstratio Mathematica, 2023 We prove that if a self-affine arc γ∈R2\gamma \in {{\mathbb{R}}}^{2} does not satisfy weak separation condition, then it is a segment of a parabola or a straight line.
Tetenov Andrei, Kutlimuratov Allanazar
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