Singularity and L2-dimension of self-similar measures

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.

► We study self-similar measures defined by iterated function systems with overlaps. ► The contraction ratios of maps are allowed to be exponentially commensurable. ► We formulate a new method to compute the L2-dimension of the measures. ► Our results allow us to determine the singularity of these measures. ► The results complement existing ones on almost everywhere absolute continuity.