On a Family of Random Noble Means Substitutions

M. Moll Fakultät für Mathematik, Universität Bielefeld, Universitätsstraße 25, D-33615 Bielefeld, Germany

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In 1989, Godrèche and Luck introduced the concept of local mixtures of primitive substitution rules along the example of the well-known Fibonacci substitution and foreshadowed heuristic results on the topological entropy and the spectral type of the diffraction measure of associated point sets. In this contribution, we present a generalisation of this concept by regarding the so-called "noble means families", each consisting of finitely many primitive substitution rules that individually all define the same two-sided discrete dynamical hull. We report about results in the randomised case on topological entropy, ergodicity of the two-sided discrete hull, and the spectral type of the diffraction measure of related point sets.

DOI: 10.12693/APhysPolA.126.539 PACS numbers: 45.30.+s, 61.44.Br