Diffraction of compatible random substitutions in one dimension

作者：Baake Michael^*; Spindeler Timo; Strungaru Nicolae

来源：Indagationes Mathematicae, 2018, 29(4): 1031-1071.

DOI：10.1016/j.indag.2018.05.008

As a guiding example, the diffraction measure of a random local mixture of the two classic Fibonacci substitutions is determined and reanalysed via self -similar measures of Hutchinson type, defined by a finite family of contractions. Our revised approach yields explicit formulas for the pure point and the absolutely continuous parts, as well as a proof for the absence of singular continuous components. This approach is then extended to the family of random noble means substitutions and, as an example with an underlying 2-adic structure, to a locally randomised version of the period doubling chain. As a first step towards a more general approach, we interpret our findings in terms of a disintegration over the Kronecker factor, which is the maximal equicontinuous factor of a covering model set.

• 出版日期2018-8