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dc.contributor.authorRiedi, Rudolf H.
Mandelbrot, Benoit
dc.creatorRiedi, Rudolf H.
Mandelbrot, Benoit 2007-10-31T01:01:16Z 2007-10-31T01:01:16Z 1998-01-15 2004-01-14
dc.description Journal Paper
dc.description.abstract In an earlier paper the authors introduced the inverse measure Âµâ  (dt) of a given measure µ(dt) on [0,1] and presented the 'inversion formula' fâ  (a) = af(1/a) which was argued to link the respective multifractal spectra of µ and Âµâ  . A second paper established the formula under the assumption that µ and Âµâ   are continuous measures. Here, we investigate the general case which reveals telling details of interest to the full understanding of multifractals. Subjecting self-similar measures to the operation µ->µ<sup>â  </sup> creates a new class of discontinuous multifractals. Calculating explicitly we find that the inversion formula holds only for the 'fine multifractal spectra' and not for the 'coarse' ones. As a consequence, the multifractal formalism fails for this class of measures. A natural explanation is found when drawing parallels to equilibrium measures of dynamical systems. In the context of our work it becomes natural to consider the degenerate Hölder exponents 0 and infinity.
dc.language.iso eng
dc.title Exceptions to the Multifractal Formalism for Discontinuous Measures
dc.type Journal article
dc.citation.bibtexName article
dc.citation.journalTitle Mathematical Proceedings Cambridge Philosophical Society 2004-01-22
dc.contributor.orgDigital Signal Processing (
dc.type.dcmi Text
dc.type.dcmi Text
dc.identifier.citation R. H. Riedi and B. Mandelbrot, "Exceptions to the Multifractal Formalism for Discontinuous Measures," Mathematical Proceedings Cambridge Philosophical Society, 1998.

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  • DSP Publications [508]
    Publications by Rice Faculty and graduate students in digital signal processing.
  • ECE Publications [1299]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students

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