SOME REMARKS ON DISCRETE APERIODIC SCHRODINGER-OPERATORS

We consider Schrodinger operators on l2(Z(v)) with deterministic aperi odic potential and Schrodinger operators on the l2-space of the set of vertices of Penrose tilings and other aperiodic self-similar tilings. The operators on l2(Z(v)) fit into the formalism of ergodic random Sc hrodinger operators. Hence, their Lyapunov exponent, integrated densit y of states, and spectrum are almost-surely constant. We show that the y are actually constant: the Lyapunov exponent for one-dimensional Sch rodinger operators with potential defined by a primitive substitution, the integrated density of states, and the spectrum in arbitrary dimen sion if the system is strictly ergodic. We give examples of strictly e rgodic Schrodinger operators that include several kinds of ''almost-pe riodic'' operators that have been studied in the literature. For Schro dinger operators on Penrose tilings we prove that the integrated densi ty of states exists and is independent of boundary conditions and the particular Penrose tiling under consideration.