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Genericity of Homeomorphisms with Full Mean Hausdorff Dimension
It is well known that the presence of horseshoes leads to positive entropy. If our goal is to construct a continuous map with infinite entropy, we...
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A Fubini-type theorem for Hausdorff dimension
It is well known that a classical Fubini theorem for Hausdorff dimension cannot hold; that is, the dimension of the intersections of a fixed set with...
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Uniformly Perfect Sets, Hausdorff Dimension, and Conformal Capacity
Using the definition of uniformly perfect sets in terms of convergent sequences, we apply lower bounds for the Hausdorff content of a uniformly...
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Hausdorff dimension regularity properties and games
The Hausdorff δ -dimension game was introduced in [2] and shown to characterize sets in ℝ d having Hausdorff dimension ≤ δ . We introduce a variation of...
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Felix Hausdorff Mathematician, Philosopher, Man of Letters
Felix Hausdorff is a singular phenomenon in the history of science. As a mathematician, he played a major role in sha** the development of modern...
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Hausdorff dimension of frequency sets in beta-expansions
By applying a recent result on the distributions of full and non-full words, we give a proof of the useful folklore result: the Hausdorff dimension...
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Examples of Ricci limit spaces with non-integer Hausdorff dimension
We give the first examples of collapsing Ricci limit spaces on which the Hausdorff dimension of the singular set exceeds that of the regular set;...
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The Hausdorff Dimension of the Spectrum of a Class of Generalized Thue-Morse Hamiltonians
Let τ be a generalized Thue-Morse substitution on a two-letter alphabet { a, b }: τ ( a ) = a m b m , τ ( b ) = b m a m for the integer m ≥ 2. Let ξ be a sequence...
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Hausdorff dimension and complex hyperbolic Schottky groups: a simplification
In the present work, we study the Hausdorff dimension of the limit set of Schottky groups on the boundary of the complex hyperbolic group via the...
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Dimension theory of Lüroth digits
We investigate the relative growth properties of the Lüroth digits and establish the Hausdorff dimension of exceptional sets of points with a given...
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Hausdorff at the Pinnacle of his Career
In 1910, Gerhard Kowalewski left Bonn to accept a full professorship at the German Technical University in Prague. This left the associate...
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The VC Dimension of Metric Balls under Fréchet and Hausdorff Distances
The Vapnik–Chervonenkis dimension provides a notion of complexity for systems of sets. If the VC dimension is small, then knowing this can...
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Map**s of Finite Area Distortion: Hausdorff Measures
In this paper we continue studying homeomorphisms of finite area distortion in the frame of Hausdorff measures.
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A Hausdorff-measure boundary element method for acoustic scattering by fractal screens
Sound-soft fractal screens can scatter acoustic waves even when they have zero surface measure. To solve such scattering problems we make what...
