Results 1 to 10 of about 65,125 (273)
Topological diagonalizations and Hausdorff dimension [PDF]
arXiv: Logic, 2002 The Hausdorff dimension of a product XxY can be strictly greater than that of Y, even when the Hausdorff dimension of X is zero. But when X is countable, the Hausdorff dimensions of Y and XxY are the same.
Tsaban, Boaz, Weiss, Tomasz
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Hausdorff Dimension and Topological Entropies of a Solenoid [PDF]
Entropy, 2020 The purpose of this paper is to elucidate the interrelations between three essentially different concepts: solenoids, topological entropy, and Hausdorff dimension.
Andrzej Biś, Agnieszka Namiecińska
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Hausdorff dimension for horseshoes [PDF]
Ergodic Theory and Dynamical Systems, 1983 AbstractWe shall measure how thick a basic set of a C1 axiom A diffeomorphism of a surface is by the Hausdorff dimension of its intersection with an unstable manifold. This depends continuously on the diffeomorphism. Generically a C2 diffeomorphism has attractors whose Hausdorff dimension is not approximated by the dimension of its ergodic measures.
Anthony Manning, Heather McCluskey
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A Survey on the Hausdorff Dimension of Intersections
Mathematical and Computational Applications, 2023 Let A and B be Borel subsets of the Euclidean n-space with dimA+dimB>n. This is a survey on the following question: what can we say about the Hausdorff dimension of the intersections A∩(g(B)+z) for generic orthogonal transformations g and translations by
Pertti Mattila
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Unimodular Hausdorff and Minkowski dimensions [PDF]
Electronic Journal of Probability, 2021 This work introduces two new notions of dimension, namely the unimodular Minkowski and Hausdorff dimensions, which are inspired from the classical analogous notions. These dimensions are defined for unimodular discrete spaces, introduced in this work, which provide a common generalization to stationary point processes under their Palm version and ...
Baccelli, François +2 more
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Quantum error correction with fractal topological codes [PDF]
Quantum, 2023 Recently, a class of fractal surface codes (FSCs), has been constructed on fractal lattices with Hausdorff dimension $2+\epsilon$, which admits a fault-tolerant non-Clifford CCZ gate \cite{zhu2021topological}.
Arpit Dua +2 more
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On the Hausdorff dimension of microsets [PDF]
Proceedings of the American Mathematical Society, 2019 We investigate how the Hausdorff dimensions of microsets are related to the dimensions of the original set. It is known that the maximal dimension of a microset is the Assouad dimension of the set. We prove that the lower dimension can analogously be obtained as the minimal dimension of a microset. In particular, the maximum and minimum exist.
Fraser, Jonathan MacDonald +3 more
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A Simple Proof of Dvoretzky-Type Theorem for Hausdorff Dimension in Doubling Spaces
Analysis and Geometry in Metric Spaces, 2022 The ultrametric skeleton theorem [Mendel, Naor 2013] implies, among other things, the following nonlinear Dvoretzky-type theorem for Hausdorff dimension: For any 0 < β < α, any compact metric space X of Hausdorff dimension α contains a subset which is ...
Mendel Manor
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The Hausdorff Dimension and Capillary Imbibition
Fractal and Fractional, 2022 The time scaling exponent for the analytical expression of capillary rise ℓ∼tδ for several theoretical fractal curves is derived. It is established that the actual distance of fluid travel in self-avoiding fractals at the first stage of imbibition is in ...
Didier Samayoa +4 more
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On the Hausdorff dimension of quasicircles [PDF]
Annales Academiae Scientiarum Fennicae Series A I Mathematica, 1987 Let \(\Gamma\) be a K-quasicircle, that is the image of a circle under a K- quasiconformal mapping of \({\mathbb{C}}\). It is shown that its Hausdorff dimension satisfies dim \(\Gamma\leq 2-K^{-3.41}\) for large K and furthermore \[ \dim \Gamma \leq 1+37[(K-1)/(K+1)]^ 2 \] for K close to 1; the square is best possible while the factor cannot be ...
J. Becker, Ch. Pommerenke
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