Lower bounds for fractal dimensions of spectral measures of the period doubling Schrödinger operator

Abstract

It is shown that there exits a lower bound $\alpha >0$ to the Hausdorff dimension of the spectral measures of the one-dimensional period doubling substitution Schrödinger operator, and, generically in the hull of such sequence, $\alpha$ is also a lower bound to the upper packing dimension of spectral measures.