This thesis explores the relationships between multifractal measures, multiplicative cascades and correlations. A review of fractal geometry, multifractal formalism and multiplicative cascades is offered. The importance of the Legendre transformation in multifractal formalism is highlighted, especially for multifractal spectrums which are not convex or twice differentiable. By reconsidering the scaling assumption $N sb{p}( alpha$) d$ alpha$ = $ sigma( alpha) rho sp{-f( alpha)} d alpha$, we show that subsets of a measure may offer a different multifractal spectrum. A gradation of self-similarity and scaling vis-a-vis canonicity is offered. Localized and generalized correlations are introduced, and two-point correlations are revisited for multiplicative cascades. A three-point correlation function is presented and discussed. The presence of an integral scale is shown to produce a more involved correlation scaling behaviour.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.56945 |
| Date | January 1992 |
| Creators | Matte, Robert |
| Contributors | Warn, Thomas (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Atmospheric and Oceanic Sciences.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001326719, proquestno: AAIMM87672, Theses scanned by UMI/ProQuest. |
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