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- Title
Spectral analysis of a family of binary inflation rules.
- Authors
Baake, Michael; Grimm, Uwe; Mañibo, Neil
- Abstract
The family of primitive binary substitutions defined by 1↦0↦01m<inline-graphic></inline-graphic> with m∈N<inline-graphic></inline-graphic> 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<inline-graphic></inline-graphic>), 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.
- Subjects
BINARY number system; SUBSTITUTION (Logic); GEOMETRIC analysis; MATHEMATICAL singularities; CONTINUOUS functions
- Publication
Letters in Mathematical Physics, 2018, Vol 108, Issue 8, p1783
- ISSN
0377-9017
- Publication type
Article
- DOI
10.1007/s11005-018-1045-4