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Singularity and L2-dimension of self-similar measures

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  • Ngai, Sze-Man

Abstract

We study self-similar measures defined by non-uniformly contractive iterated function systems of similitudes with overlaps. In the case the contraction ratios of the similitudes are exponentially commensurable, we describe a method to compute the L2-dimension of the associated self-similar measures. Our result allows us to determine the singularity of some of such measures.

Suggested Citation

  • Ngai, Sze-Man, 2012. "Singularity and L2-dimension of self-similar measures," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 256-265.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:3:p:256-265
    DOI: 10.1016/j.chaos.2011.12.010
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    Cited by:

    1. Jaroszewska, Joanna, 2013. "A note on iterated function systems with discontinuous probabilities," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 28-31.

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