The spectrum of a quasiperiodic Schroedinger operator

The spectrum σ(H) of the tight binding Fibonacci Hamiltonian (Hmn=δm,n+1+δm+1,n+δm,nμν(n), 1/ω is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any μ, and σ(H) is a Cantor set for vertical strokeμvertical stroke≥4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for vertical strokeμvertical stroke≥16. (orig.)