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Étude du formalisme multifractal pour les fonctions

Abstract : The aim of this thesis is the multifractal analysis of selfsimilar functions and the study of the validity of the multifractal formalism. First, we determine the exact pointwise Hölder regularity for functions such that locally the graph is roughly a contraction of the global graph, modulo an error; then we compute the Hausdorff dimensions of the sets of points which have the same Hölder exponent; and finally we verify the conjectures of Frish and Parisi and the one of Arneodo, Bacry and Muzy, which relate these dimensions to some averaged quantities extracted from the function. We study different types of selfsimilarities, and prove (by reformuling some times) that the wavelet analysis is a good tool to study the validity of these relations.
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Submitted on : Thursday, February 24, 2011 - 9:56:21 AM
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  • HAL Id : pastel-00569006, version 1



Mourad Ben Slimane. Étude du formalisme multifractal pour les fonctions. Analyse fonctionnelle [math.FA]. Ecole Nationale des Ponts et Chaussées, 1996. Français. ⟨pastel-00569006⟩



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