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Multifractal formalism and anisotropic selfsimilar functions

Published online by Cambridge University Press:  01 September 1998

MOURAD BEN SLIMANE
MOURAD BEN SLIMANE
Affiliation:
Département de Mathématiques, Faculté des Sciences de Tunis, 1060 Campus Universitaire, Tunis, Tunisie
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Abstract

In this paper we prove that the conjectures of Frisch and Parisi and Arneodo et al. (called the multifractal formalism for functions) may fail for some non-homogeneous selfsimilar functions on ℝ2. In these cases, we compute the correct spectrum of singularities and we show how the multifractal formalism must be modified.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 124 , Issue 2 , September 1998 , pp. 329 - 363
Copyright
Cambridge Philosophical Society 1998

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