The singular continuous diffraction measure of the Thue-Morse chain

Details The singular continuous diffraction measure of the Thue-Morse chain The singular continuous diffraction measure of the Thue-Morse chain

2008-09-03

arxiv.org/abs/0809.0580v2

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.

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