Results 11 to 20 of about 1,490 (75)
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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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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Non-existence of multi-line Besicovitch sets [PDF]
, 2013 If a compact set K \subset R^2 contains a positive-dimensional family of line-segments in positively many directions, then K has positive measure.Comment: 7 pages.
Orponen, Tuomas
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A note on the 1-prevalence of continuous images with full Hausdorff dimension [PDF]
, 2014 We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. It is known that for a prevalent (in the sense of Hunt, Sauer and Yorke) set of functions the Hausdorff dimension of the image is as large ...
Fraser, Jonathan M., Hyde, James T.
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Packing-Dimension Profiles and Fractional Brownian Motion [PDF]
, 2007 In order to compute the packing dimension of orthogonal projections Falconer and Howroyd (1997) introduced a family of packing dimension profiles ${\rm Dim}_s$ that are parametrized by real numbers $s>0$.
DAVAR KHOSHNEVISAN +4 more
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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
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Existence results for nonlinear elliptic problems on fractal domains
Advances in Nonlinear Analysis, 2016 Some existence results for a parametric Dirichlet problem defined on the Sierpiński fractal are proved. More precisely, a critical point result for differentiable functionals is exploited in order to prove the existence of a well-determined open interval
Ferrara Massimiliano +2 more
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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
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