Real Analysis Exchange

Multifractals and the Dimension of Exceptions

Károly Simon

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Abstract

We consider a one parameter family of self-similar sets of overlapping construction. We study the exceptional set; that is the set of those parameters for which the correlation dimension is smaller than the similarity dimension. We find a connection between the exceptional set and the multifractal analysis of a measure.

Article information

Source
Real Anal. Exchange, Volume 27, Number 1 (2001), 191-208.

Dates
First available in Project Euclid: 6 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1212763960

Mathematical Reviews number (MathSciNet)
MR1887691

Zentralblatt MATH identifier
1018.28006

Subjects
Primary: 28A78: Hausdorff and packing measures
Secondary: 28A80: Fractals [See also 37Fxx]

Keywords
multifractal analysis exceptional set

Citation

Simon, Károly. Multifractals and the Dimension of Exceptions. Real Anal. Exchange 27 (2001), no. 1, 191--208. https://projecteuclid.org/euclid.rae/1212763960


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References

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