Renormalization operator for substitutions (Q6607749)
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scientific article; zbMATH DE number 7915645
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Renormalization operator for substitutions |
scientific article; zbMATH DE number 7915645 |
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Renormalization operator for substitutions (English)
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18 September 2024
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\textit{H. Bruin} and \textit{R. Leplaideur} [Commun. Math. Phys. 321, No. 1, 209--247 (2013; Zbl 1271.82017)] studied thermodynamic formalism for a class of renormalizable dynamical systems generated by the Thue-Morse substitution (and in complex dynamics by the Feigenbaum-Coullet-Tresser map), finding phase transitions exhibited in certain fixed points of the renormalization operator. Here these renormalization operators for potentials in symbolic dynamics are studied in the more general setting of marked substitutions, and properties of fixed directions for the renormalization operator are elucidated.
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thermodynamic formalism
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substitutions
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renormalization
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grounds states
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quasi-crystals
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