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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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Topological diagonalizations and Hausdorff dimension [PDF]
, 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 of recurrence sets [PDF]
Nonlinearity, 2023 We consider linear mappings on the 2-dimensional torus, defined by T(x)=Ax (mod 1) , where A is an invertible 2×2 integer matrix, with no eigenvalues on the unit circle. In the case detA=±1 , we give a formula for the Hausdorff dimension of the set {x∈T2:
Zhang-nan Hu, T. Persson
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On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane [PDF]
Duke mathematical journal, 2021 Let $0 \leq s \leq 1$ and $0 \leq t \leq 2$. An $(s,t)$-Furstenberg set is a set $K \subset \mathbb{R}^{2}$ with the following property: there exists a line set $\mathcal{L}$ of Hausdorff dimension $\dim_{\mathrm{H}} \mathcal{L} \geq t$ such that $\dim_{\
Tuomas Orponen, Pablo Shmerkin
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A Lorentzian analog for Hausdorff dimension and measure [PDF]
Pure and Applied Analysis, 2021 We define a one-parameter family of canonical volume measures on Lorentzian (pre-)length spaces. In the Lorentzian setting, this allows us to define a geometric dimension - akin to the Hausdorff dimension for metric spaces - that distinguishes between e ...
R. McCann, Clemens Samann
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Hausdorff dimension, heavy tails, and generalization in neural networks [PDF]
Neural Information Processing Systems, 2020 Despite its success in a wide range of applications, characterizing the generalization properties of stochastic gradient descent (SGD) in non-convex deep learning problems is still an important challenge.
Umut Simsekli +3 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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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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Wild solutions of the Navier–Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1 [PDF]
Journal of the European Mathematical Society (Print), 2018 We prove non-uniqueness for a class of weak solutions to the Navier-Stokes equations which have bounded kinetic energy, integrable vorticity, and are smooth outside a fractal set of singular times with Hausdorff dimension strictly less than 1.
T. Buckmaster, Maria Colombo, V. Vicol
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