On the correlation dimension of the spectral measure for the Thue-Morse sequence (Q1285081)
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scientific article; zbMATH DE number 1279586
| Language | Label | Description | Also known as |
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| English | On the correlation dimension of the spectral measure for the Thue-Morse sequence |
scientific article; zbMATH DE number 1279586 |
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On the correlation dimension of the spectral measure for the Thue-Morse sequence (English)
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17 September 1999
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The spectral measure of the classical Thue--Morse sequence is singular and continuous. \textit{C. Godrèche} and \textit{J. M. Luck} [J. Phys. A, Math. Gen. 23, 3769-3797 (1990; Zbl 0713.11021)] obtained numerical estimates for the generalized dimensions \(D_q\) of the sequence. Here exact formulae for the autocorrelation function are used to compute \(D_2\) (the correlation dimension) exactly.
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singular continuous spectrum
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autocorrelation function
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spectral measure
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Thue-Morse sequence
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