Multifractal Structure of Convolution of the Cantor Measure
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 μ. By using some combinatoric techniques, we show that the set E of at...
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Veröffentlicht in: | Advances in applied mathematics 2001-07, Vol.27 (1), p.1-16 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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 μ. By using some combinatoric techniques, we show that the set
E of attainable local dimensions of μ 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. |
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ISSN: | 0196-8858 1090-2074 |
DOI: | 10.1006/aama.2000.0683 |