Singularity and L2-dimension of self-similar measures

Sze-Man Ngai

Chaos, Solitons & Fractals, 2012, vol. 45, issue 3, 256-265

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:45:y:2012:i:3:p:256-265

DOI: 10.1016/j.chaos.2011.12.010

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