Name
Abstract | ||
|---|---|---|
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 @m. By using some combinatoric techniques, we show that the set E of attainable local dimensions of @m 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. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1006/aama.2000.0683 | Advances in Applied Mathematics |
Keywords | Field | DocType |
iterated function system,multifractal structure,isolated point,open set condition,cantor measure,m-time convolution,local dimension,multifractal formalism,attainable local dimension,combinatoric technique,set e,representation,convolution,satisfiability,multifractal,probability | Iterated function system,Discrete mathematics,Combinatorics,Convolution,Mathematical analysis,Measure (mathematics),Fractal,Isolated point,Probability theory,Mathematics,Multifractal system,Open set | Journal |
Volume | Issue | ISSN |
27 | 1 | 0196-8858 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tian-You Hu | 1 | 0 | 1.01 |
| Ka-Sing Lau | 2 | 6 | 2.48 |