Singular continuous electron spectrum for a class of circle sequences

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Abstract
We derive substitution rules for a class of binary quasiperiodic sequences generated by circle maps whose rotation numbers are obtained from the precious means. The nature of the electron spectra for the corresponding diatomic chains is studied in the nearest-neighbour on-site tight-binding approximation using the transfer-matrix technique. By studying properties of the trace maps, we find that the spectrum is purely singular continuous in most of the studied cases.