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It is shown that there exits a lower bound $\alpha>0$ to the Hausdorffdimension of the spectral measures of the one-dimensional period doublingsubstitution Schr\"odinger operator, and, generically in the hull of suchsequence, $\alpha$ is also a lower bound to the upper packing dimension ofspectral measures.

Lower bounds for fractal dimensions of spectral measures of the period doubling Schr\"odinger operator