Substitution-based structures with absolutely continuous spectrum
arXiv:1706.05289 · doi:10.1016/j.indag.2018.05.009
Abstract
By generalising Rudin's construction of an aperiodic sequence, we derive new substitution-based structures which have purely absolutely continuous diffraction and mixed dynamical spectrum, with absolutely continuous and pure point parts. We discuss several examples, including a construction based on Fourier matrices which yields constant-length substitutions for any length.
13 pages