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• W1989468930 abstract "We introduce and develope a unifying multifractal framework. The framework developed in this paper is based on the notion of deformations of empirical measures. This approach leads to significant extensions of already know results. However, our approach not only leads to extensions of already know results, but also, by considering non-linear deformations, provides the basis for the study of several new and non-linear local characteristic. We also initiate a detailed study of the fractal structure of so-called divergence points. We define multifractal spectra that provides extremely precise quantitative information about the distribution of individual divergence points of arbitrary (possibly non-linear) deformations, thereby extending and unifying many diverse qualitative results on the behaviour of divergence points. The techniques used in proving the main results are taken from large deviation theory and are completely different from previous techniques in the literature. Nous introduisons et développons un cadre multifractal unificateur. Le cadre développé dans cet article utilise la notion de déformations de mesures empiriques. Cette approche aboutit à des extensions significatives de résultats déjà connus. Pourtant, notre approche, non seulement aboutit aux extensions des résultats déjà connus, mais procure également, en considérant des déformations non-linéaires, la base pour l'étude de plusieurs nouvelles charactéristiques locales non-linéaires. Nous introduisons également une étude détaillée de la structure fractale des “points de divergence”. Nous définissons des spectres multifractals qui apportent une information quantitative extrêmement précise sur la distribution de points de divergence individuels de déformation arbitraire (y compris non-linéaire), et ainsi nous étendons et unifions de nombreux résultats qualitatifs variés sur le comportement des points de divergence. Les techniques utilisées pour démontrer les principaux résultats sont issues de la théorie des grandes déviations et sont complètement différentes des techniques utilisées précédemment dans la littérature." @default.
• W1989468930 created "2016-06-24" @default.
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• W1989468930 date "2003-12-01" @default.
• W1989468930 modified "2023-09-29" @default.
• W1989468930 title "Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages" @default.
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• W1989468930 doi "https://doi.org/10.1016/j.matpur.2003.09.007" @default.
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