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首页> 外文期刊>Annales Henri Poincare >Spectral Properties of Schrodinger Operators Associated with Almost Minimal Substitution Systems
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Spectral Properties of Schrodinger Operators Associated with Almost Minimal Substitution Systems

机译：与几乎最小替代系统相关的Schrodinger运算符的光谱特性

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We study the spectral properties of ergodic Schrodinger operators that are associated with a certain family of non-primitive substitutions on a binary alphabet. The corresponding subshifts provide examples of dynamical systems that go beyond minimality, unique ergodicity and linear complexity. In some parameter region, we are naturally in the setting of an infinite ergodic measure. The almost sure spectrum is singular and contains an interval. We show that under certain conditions, eigenvalues can appear. Some criteria for the exclusion of eigenvalues are fully characterized, including the existence of strongly palindromic sequences. Many of our structural insights rely on return word decompositions in the context of non-uniformly recurrent sequences. We introduce an associated induced system that is conjugate to an odometer.
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