We will discuss a dynamical approach by Qinghui Liu and Yanhui Qu to study the spectrum of the Thue-Morse Hamiltonian, a Schrodinger operator on l^2. They use the trace map formalism to describe the spectrum, and study the corresponding polynomials to characterize subsets of their zeros that converge to a Cantor set. In doing this they establish bounds of the Hausdorff dimension. We will also discuss a possiblility to obtain similar bounds on the thickness of the spectrum.