𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Multifractal Structure of Convolution of the Cantor Measure

✍ Scribed by Tian-You Hu; Ka-Sing Lau

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
138 KB
Volume
27
Category
Article
ISSN
0196-8858

No coin nor oath required. For personal study only.

✦ Synopsis

The multifractal structure of measures generated by iterated function systems (IFS) with overlaps is, to a large extend, unknown. In this paper we study the local dimension of the m-time convolution of the standard Cantor measure Β΅. By using some combinatoric techniques, we show that the set E of attainable local dimensions of Β΅ contains an isolated point. This is rather surprising because when the IFS satisfies the open set condition, the set E is an interval. The result implies that the multifractal formalism fails without the open set condition.

πŸ“œ SIMILAR VOLUMES

The Multifractal Structure of Arterial T
The Multifractal Structure of Arterial Trees
✍ J. GRASMAN; J.W. BRASCAMP; J.L. VAN LEEUWEN; B. VAN PUTTEN πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 188 KB

Fractal properties of arterial trees are analysed using the cascade model of turbulence theory. It is shown that the branching process leads to a non-uniform structure at the micro-level meaning that blood supply to the tissue varies in space. From the model it is concluded that, depending on the br

Exact packing measure of linear Cantor s
Exact packing measure of linear Cantor sets
✍ De–Jun Feng πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 163 KB

Let K be the attractor of a linear iterated function system Sj x = ρjx + bj (j = 1, . . . , m) on the real line satisfying the open set condition (where the open set is an interval). It is well known that the packing dimension of K is equal to α, the unique positive solution y of the equation m j=1

The Multifractal Spectrum of Quasi Self-
The Multifractal Spectrum of Quasi Self-Similar Measures
✍ Toby C O'Neil πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 305 KB

We define the notion of quasi self-similar measures and show that for such measures their generalised Hausdorff and packing measures are positive and finite at the critical exponent. In practice this allows easy calculation of their dimension functions. We then show that a coarse form of the multifr