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Multifractal formalisms: Boxed versus centered intervals

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Analysis in Theory and Applications

Abstract

There are mainly two approaches to the multifractal analysis of measures. The first one, which is used in applications and in studying problems arising from dynamical systems, uses a hierarchy of boxes. The second one, which is more satisfactory from the viewpoint of geometric measure theory, uses more intrinsic concepts. This article is an account of a work by J. Barral, F. Ben Nasr, and J. Peyriére [3] which provides a bridge between these two theories.

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Authors and Affiliations

  1. Université Paris-Sud CNRS UMR 8628, Mathématiques bât 425, 91405, Orsay Cedex, France

    Jacques Peyriére

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  1. Jacques Peyriére
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Correspondence to Jacques Peyriére.

Additional information

This paper was presented in the Fraetal Satellite Conference of ICM 2002 in Nanjing.

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Peyriére, J. Multifractal formalisms: Boxed versus centered intervals. Anal. Theory Appl. 19, 332–341 (2003). https://doi.org/10.1007/BF02835532

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  • DOI: https://doi.org/10.1007/BF02835532

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