The singular continuous diffraction measure of the Thue-Morse chain

Baake, Michael and Grimm, Uwe (2008). The singular continuous diffraction measure of the Thue-Morse chain. Journal of Physics A: Mathematical and Theoretical, 41(42) p. 422001.

DOI: https://doi.org/10.1088/1751-8113/41/42/422001

Abstract

The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the Thue-Morse chain, in its realization as a binary sequence with values in ±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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