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Multifractal formalism for self-affine measures with overlaps

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Abstract.

We prove that for a class of self-affine measures defined by an expanding matrix whose eigenvalues have the same modulus, the Lq-spectrum τ(q) is differentiable for all q > 0. Furthermore, we prove that the multifractal formalism holds in the region corresponding to q > 0.

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Authors and Affiliations

  1. Department of Mathematics, Fujian Normal University, Fuzhou, 350007, China

    Qi-Rong Deng

  2. Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460-8093, USA

    Sze-Man Ngai

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  1. Qi-Rong Deng
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  2. Sze-Man Ngai
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Correspondence to Qi-Rong Deng.

Additional information

Received: 4 August 2008, Revised: 19 January 2009

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Deng, QR., Ngai, SM. Multifractal formalism for self-affine measures with overlaps. Arch. Math. 92, 614–625 (2009). https://doi.org/10.1007/s00013-009-2969-9

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  • DOI: https://doi.org/10.1007/s00013-009-2969-9

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