95-456 Bovier A., Ghez J.-M.

Schr\"odinger operators generated by substitutions (12K, TeX) Oct 12, 95

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Abstract. In the framework of the theoretical study of quasi-crystals, we consider one-dimensional Schr\"odinger operators with potentials generated by primitive substitutions. First, we give the general construction of the trace map of their associated transfer matrices. Then, under an algorithmically verifiable hypothesis, we prove that their spectrum is singular continuous and supported on a Cantor set of zero Lebesgue measure. Finally, we apply this result to some examples.

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