Singular continuous spectrum for the period doubling Hamiltonian on a set of full measure

We consider the discrete one-dimensional Schroedinger operator with potential generated by the period doubling substitution. We show that for almost every element in the hull O, with respect to the unique ergodic measure μ on O, there are no eigenvalues. Combining this with a result proven by Kotani, we establish purely singular continuous spectrum on a set of full measure. (orig.)