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Wavelet Analysis of Fractal Boundaries. Part 2: Multifractal Analysis

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Abstract

This second part deals with the global analysis of the boundary of domains . We develop methods for determining the dimensions of the sets where the local behaviors introduced in Part 1 occur. These methods are based on analogies with the thermodynamic formalism in statistical physics and lead to new classification tools for fractal domains.

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Authors and Affiliations

  1. Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris XII, 61 Avenue du Général de Gaulle, 94010, Créteil Cedex, France

    Stéphane Jaffard

  2. LATP, CMI, Université de Provence 39 rue F. Joliot-Curie, 13453, Marseille Cedex 13, France

    Clothilde Mélot

Authors
  1. Stéphane Jaffard
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  2. Clothilde Mélot
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Correspondence to Stéphane Jaffard.

Additional information

Communicated by M. B. Ruskai

The first author is supported by the Institut Universitaire de France.

This work was performed while the second author was at the Laboratoire d’Analyse et de Mathématiques Appliquées (University Paris XII) and at the Istituto di Matematica Applicata e Tecnologie Informatiche (Pavia, Italy) and partially supported by the Société de Secours des amis des Sciences and the TMR Research Network “Breaking Complexity”.

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Jaffard, S., Mélot, C. Wavelet Analysis of Fractal Boundaries. Part 2: Multifractal Analysis. Commun. Math. Phys. 258, 541–565 (2005). https://doi.org/10.1007/s00220-005-1353-2

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  • DOI: https://doi.org/10.1007/s00220-005-1353-2

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