 9398 Anton Bovier , JeanMichel Ghez
 Spectral properties of onedimensional Schr\"odinger operators
generated by substitutions
(65K, TeX)
Apr 27, 93

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Abstract. We investigate onedimensional discrete Schr\"odinger
operators whose potentials are invariant under a substitution rule. The
spectral properties of these operators can be obtained from the analysis
of a dynamical system, called the trace map. We give a careful derivation
of these maps in the general case and exhibit some specific properties.
Under an additional, easily verifiable hypothesis concerning the
structure of the trace map we present an analysis of their dynamical
properties that allows us to prove that the spectrum of the underlying
Schr\"odinger operator is singular and supported on a set of zero
Lebesgue measure. A condition allowing to exclude point spectrum is also
given. The application of our theorems is explained on a series of
examples.
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