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Multifractal Formalism for Almost all Self-Affine Measures

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Abstract

We conduct the multifractal analysis of self-affine measures for “almost all” family of affine maps. Besides partially extending Falconer’s formula of L q-spectrum outside the range 1 < q ≤ 2, the multifractal formalism is also partially verified.

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Authors and Affiliations

  1. LAGA (UMR 7539), Département de Mathématiques, Institut Galilée, Université Paris 13, 99 Avenue Jean-Baptiste Clément, 93430, Villetaneuse, France

    Julien Barral

  2. Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong

    De-Jun Feng

Authors
  1. Julien Barral
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  2. De-Jun Feng
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Correspondence to De-Jun Feng.

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Communicated by G. Gallavotti

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Barral, J., Feng, DJ. Multifractal Formalism for Almost all Self-Affine Measures. Commun. Math. Phys. 318, 473–504 (2013). https://doi.org/10.1007/s00220-013-1676-3

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  • DOI: https://doi.org/10.1007/s00220-013-1676-3

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