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12
Aperiodic order via dynamical systems: Diffraction for sets of finite local complexity
, 2007
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On a family of random noble means substitutions
"... In 1989, Godrèche and Luck introduced the concept of local mixtures of primitive substitution rules along the example of the wellknown Fibonacci substitution and foreshadowed heuristic results on the topological entropy and the spectral type of the diffraction measure of associated point sets. In t ..."
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In 1989, Godrèche and Luck introduced the concept of local mixtures of primitive substitution rules along the example of the wellknown 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 socalled noble means families, each consisting of finitely many primitive substitution rules that individually all define the same twosided discrete dynamical hull. We report about results in the randomised case on topological entropy, ergodicity of the twosided discrete hull, and the spectral type of the diffraction measure of related point sets.
APERIODIC ORDER AND PURE POINT DIFFRACTION
, 2008
"... We give a leisurely introduction into mathematical diffraction theory with a focus on pure point diffraction. In particular, we discuss various characterisations of pure point diffraction and common models arising from cut and project schemes. We finish with a list of open problems. ..."
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We give a leisurely introduction into mathematical diffraction theory with a focus on pure point diffraction. In particular, we discuss various characterisations of pure point diffraction and common models arising from cut and project schemes. We finish with a list of open problems.
Equicontinuous factors, proximality and Ellis semigroup for Delone sets
, 2014
"... 2.1 General background........................... 6 2.2 Background on dynamical systems................... 6 ..."
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2.1 General background........................... 6 2.2 Background on dynamical systems................... 6
is its (unimodular) substitution matrix. The family
"... In 1989, Godrèche and Luck [1] introduced the concept of local mixtures of primitive substitution rules along the example of the wellknown Fibonacci substitution and foreshadowed heuristic results on the topological entropy and the spectral type of the diffraction measure of associated point sets. ..."
Abstract
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In 1989, Godrèche and Luck [1] introduced the concept of local mixtures of primitive substitution rules along the example of the wellknown 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 socalled ‘noble means families’, each consisting of finitely many primitive substitution rules that individually all define the same twosided discrete dynamical hull. We report about results in the randomised case on topological entropy, ergodicity of the twosided discrete hull, and the spectral type of the diffraction measure of related point sets.