Divergence points of self-similar measures and packing dimension (Q2642051)

Considering a self-similar measure \(M\) on \(\mathbb{R}^d\), we call a point \(x\in\mathbb{R}^d\) a divergence point if and only if \(\lim_{r\searrow 0} {\log M(B(x, r))\over\log r}\) does not exist, here \(B(x,r)\) is a ball. The authors investigate the packing dimension of divergence points of self-similar measures. The result shows that, except for certain trivial cases, many natural set of divergence points have distinct Hausdorff and packing dimensions.