Renormalization analysis of correlation properties in a quasiperiodically forced two-level system: quadratic irrationals

B. Mestel, Andrew Osbaldestin

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Abstract

Generalizing from the case of golden mean frequency to a wider class of quadratic irrationals, we extend our renormalization analysis of the self-similarity of correlation functions in a quasiperiodically forced two-level system. We give a description of all piecewise-constant periodic orbits of an additive functional recurrence generalizing that present in the golden mean case. We establish a criterion for periodic orbits to be globally bounded, and also calculate the asymptotic height of the main peaks in the correlation function.
Original languageEnglish
Pages (from-to)8969-8989
Number of pages21
JournalJournal of Physics A: Mathematical and General
Volume37
Issue number8
DOIs
Publication statusPublished - Sep 2004

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