PUB - Publikationen an der Universität Bielefeld

This work focuses on several models of aperiodic order and their applications in different areas of mathematics and mathematical physics. After a short introduction to the theory of dynamicals systems, we present random substitutions as a stochastic variant of substitutions which create symbolic dynamical systems that combine long-range order with a positive entropy. Using renormalization techniques, we obtain expressions for the entropy, diffraction, and ergodic measures of such systems. In the second part, we investigate spectral properties of Schrödinger operators that are associated with non-primitive substitution systems and dynamically defined product systems. Finally we perform a multifractal analysis of a particular spectral measure that has become known as the Thue--Morse measure.