一类二元膨胀定则的谱分析
Spectral analysis of a family of binary inflation rules
摘要：
研究了由$1 \mapsto 0 \mapsto 0 1^m$与$m\in\mathbb{N}$定义的本原二元置换族.相应的衍射措施的光谱类型进行了分析，其几何实现与prototiles（间隔）的自然长度。除了著名的斐波那契膨胀（$m=1$），膨胀规则要么有整数膨胀因子，但长度不恒定，要么是非Pisot类型。我们证明了它们都有奇异衍射，或者是纯点型的，或者是本质上奇异连续的。
英文摘要：
The family of primitive binary substitutions defined by $1 \mapsto 0 \mapsto 0 1^m$ with $m\in\mathbb{N}$ is investigated. The spectral type of the corresponding diffraction measure is analysed for its geometric realisation with prototiles (intervals) of natural length. Apart from the well-known Fibonacci inflation ($m=1$), the inflation rules either have integer inflation factors, but non-constant length, or are of non-Pisot type. We show that all of them have singular diffraction, either of pure point type or essentially singular continuous.
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