Discrete self-similar multifractals with examples from algebraic number theory
Extremely non-normal continued fractions
Distribution of digits in integers: fractal dimensions and zeta functions
Characterization of local dimension functions of subsets of
For a subset and , the local Hausdorff dimension function of E at x is defined by where denotes the Hausdorff dimension. We give a complete characterization of the set of functions that are local Hausdorff dimension functions. In fact, we prove a significantly more general result, namely, we give a complete characterization of those functions that are local dimension functions of an arbitrary regular dimension index.
Typical multifractal box dimensions of measures
We study the typical behaviour (in the sense of Baire’s category) of the multifractal box dimensions of measures on . We prove that in many cases a typical measure μ is as irregular as possible, i.e. the lower multifractal box dimensions of μ attain the smallest possible value and the upper multifractal box dimensions of μ attain the largest possible value.
A Variational Principle for the Hausdorff Dimension of Fractal Sets.
Corona C*-algebras and their applications to lifting problems.
Iterated Cesàro averages, frequencies of digits, and Baire category
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