English

The singular continuous diffraction measure of the Thue-Morse chain

Dynamical Systems 2008-10-06 v2 Mathematical Physics math.MP

Abstract

The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the Thue-Morse chain, in its realisation as a binary sequence with values in {±1}\{\pm 1\}. We revisit this example and derive a functional equation together with an explicit form of the corresponding singular continuous diffraction measure, which is related to the known representation as a Riesz product.

Cite

@article{arxiv.0809.0580,
  title  = {The singular continuous diffraction measure of the Thue-Morse chain},
  author = {Michael Baake and Uwe Grimm},
  journal= {arXiv preprint arXiv:0809.0580},
  year   = {2008}
}

Comments

6 pages, 1 figure; revised and improved version

R2 v1 2026-06-21T11:16:24.796Z