Results 1 to 10 of about 1,334 (116)
Dimension of the intersection of certain Cantor sets in the plane [PDF]
Opuscula Mathematica, 2021 In this paper we consider a retained digits Cantor set \(T\) based on digit expansions with Gaussian integer base. Let \(F\) be the set all \(x\) such that the intersection of \(T\) with its translate by \(x\) is non-empty and let \(F_{\beta}\) be the ...
Steen Pedersen, Vincent T. Shaw
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Computability of Self‐Similar Sets [PDF]
Mathematical Logic Quarterly, 1999 AbstractWe investigate computability of a self‐similar set on a Euclidean space. A nonempty compact subset of a Euclidean space is called a self‐similar set if it equals to the union of the images of itself by some set of contractions. The main result in this paper is that if all of the contractions are computable, then the self‐similar set is a ...
Hiroyasu Kamo, Kiko Kawamura
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Optimized Self-Similar Borel Summation
Axioms, 2023 The method of Fractional Borel Summation is suggested in conjunction with self-similar factor approximants. The method used for extrapolating asymptotic expansions at small variables to large variables, including the variables tending to infinity, is ...
Simon Gluzman, Vyacheslav I. Yukalov
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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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Elementary Fractal Geometry. 2. Carpets Involving Irrational Rotations
Fractal and Fractional, 2022 Self-similar sets with the open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in the plane, based on rotation by irrational angles.
Christoph Bandt, Dmitry Mekhontsev
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Multiple codings of self-similar sets with overlaps [PDF]
Advances in Applied Mathematics, 2021 In this paper we consider a general class $\mathcal E$ of self-similar sets with complete overlaps. Given a self-similar iterated function system $Φ=(E, \{f_i\}_{i=1}^m)\in\mathcal E$ on the real line, for each point $x\in E$ we can find a sequence $(i_k)=i_1i_2\ldots\in\{1,\ldots,m\}^\mathbb N$, called a coding of $x$, such that $$ x=\lim_{n\to\infty ...
Karma Dajani +4 more
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A New Proof and Consequences of the Fixed Point Theorem of Matkowski
Annales Mathematicae Silesianae, 2021 In this work it was proved Matkowski’s fixed point theorem. The consequences of this theorem are also presented.
Barcz Eugeniusz
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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
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Mathematics, 2021 The Lattice String Approximation algorithm (or LSA algorithm) of M. L. Lapidus and M. van Frankenhuijsen is a procedure that approximates the complex dimensions of a nonlattice self-similar fractal string by the complex dimensions of a lattice self ...
Michel L. Lapidus +2 more
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A p.c.f. self-similar set with no self-similar energy [PDF]
Journal of Fractal Geometry, Mathematics of Fractals and Related Topics, 2019 An example of a p.c.f. ( post-critically finite ) self-similar set without eigenform for any set of weights, is provided. The existence of an eigenform on such sets was an important, long-standing open problem in analysis on fractals.
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