Mathematics – Dynamical Systems
Scientific paper
2008-09-03
J. Phys. A: Math. Theor. 41 (2008) 422001 (6pp)
Mathematics
Dynamical Systems
6 pages, 1 figure; revised and improved version
Scientific paper
10.1088/1751-8113/41/42/422001
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 $\{\pm 1\}$. 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.
Baake Michael
Grimm Uwe
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