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Discrete self-similar multifractals with examples from algebraic number theory

L. Olsen — 2006

Acta Arithmetica

Extremely non-normal continued fractions

L. Olsen — 2003

Acta Arithmetica

Distribution of digits in integers: fractal dimensions and zeta functions

L. Olsen — 2002

Acta Arithmetica

Characterization of local dimension functions of subsets of $ℝ^{d}$

L. Olsen — 2005

Colloquium Mathematicae

For a subset $E \subseteq ℝ^{d}$ and $x \in ℝ^{d}$ , the local Hausdorff dimension function of E at x is defined by $d i m_{H, l o c} (x, E) = l i m_{r ↘ 0} d i m_{H} (E \cap B (x, r))$ where $d i m_{H}$ 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

L. Olsen — 2011

Fundamenta Mathematicae

We study the typical behaviour (in the sense of Baire’s category) of the multifractal box dimensions of measures on $ℝ^{d}$ . 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.

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Currently displaying 1 – 8 of 8

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 $ℝ^{d}$

Typical multifractal box dimensions of measures

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