Exceptions to the Multifractal Formalism for Discontinuous Measures
| dc.citation.bibtexName | article | en_US |
| dc.citation.journalTitle | Mathematical Proceedings Cambridge Philosophical Society | en_US |
| dc.contributor.author | Riedi, Rudolf H. | en_US |
| dc.contributor.author | Mandelbrot, Benoit | en_US |
| dc.contributor.org | Digital Signal Processing (http://dsp.rice.edu/) | en_US |
| dc.date.accessioned | 2007-10-31T01:01:16Z | |
| dc.date.available | 2007-10-31T01:01:16Z | |
| dc.date.issued | 1998-01-15 | en |
| dc.date.modified | 2004-01-22 | en_US |
| dc.date.submitted | 2004-01-14 | en_US |
| dc.description | Journal Paper | en_US |
| dc.description.abstract | In an earlier paper the authors introduced the <i>inverse measure</i> <i>µ</i><sup>â </sup>(<i>dt</i>) of a given measure <i>µ</i>(<i>dt</i>) on [0,1] and presented the 'inversion formula' <i>f</i><sup>â </sup>(<i>a</i>) = <i>a</i><i>f</i>(1/<i>a</i>) which was argued to link the respective multifractal spectra of <i>µ</i> and <i>µ</i><sup>â </sup>. A second paper established the formula under the assumption that <i>µ</i> and <i>µ</i><sup>â </sup> 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 <i>µ</i>-><i>µ</i><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. | en_US |
| dc.identifier.citation | R. H. Riedi and B. Mandelbrot, "Exceptions to the Multifractal Formalism for Discontinuous Measures," <i>Mathematical Proceedings Cambridge Philosophical Society,</i> 1998. | |
| dc.identifier.uri | https://hdl.handle.net/1911/20270 | |
| dc.language.iso | eng | |
| dc.subject | Temporary | * |
| dc.subject.keyword | Temporary | en_US |
| dc.subject.other | Multifractals | en_US |
| dc.title | Exceptions to the Multifractal Formalism for Discontinuous Measures | en_US |
| dc.type | Journal article | |
| dc.type.dcmi | Text |
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